Field mapping of ballistic pressure pulse sources

1 Introduction

Since the introduction of extracorporeal shockwave lithotripsy (ESWL) for the treatment of kidney stones in the 90th the shockwave technology is augmented to a variety of other fields. One of these fields is the application of focused low energy shockwaves - also known as Extra-corporeal Shockwave Therapy (ESWT) - in the treatment of musculoskeletal disorders [11]. During the in vivo evaluation of potential unwanted side effects of ESWL in the 80th, shockwave induced osteoblast stimulation and bone apposition after an initial osteocyte-damage was observed [17, 21]. This marks the initiation of shockwave therapy for the treatment of pseudarthrosis [21]. Nowadays the ESWT is a standard method in orthopedics for the treatment of epicondylitis, calcific tendinitis, achillodynia and calcaneal spur. Newly application are found in the treatment of myofascial pain with trigger-point-therapy [7]. Clinical trials report good results without significant side effects [7, 8, 11, 15, 17, 20]. Therapeutic success with such amount of different indications suggest the assumption that there must be many different bio-effects related with shockwave therapy [21]. Ballistic pressure pulse sources use the same principle as air guns. Pressurized air (typically 2 − 4 Bar) is used to accelerate a cylindrical steel projectile (typical weight 3 g) guided through a tube of about 20 cm onto the rear face of a conical waveguide, calledapplicator. Typical diameter of an applicator on the patient side is 15 mm with a weight of 30 g. Other applicators with different diameters (6 mm − 36 mm), shapes (convex or concave end-surface) and lengths can be attached to the hand-piece. After the impact of the projectile on the applicator a compression wave travels through the material and is transferred at the adjacent side into the patient via a coupling gel [24, 27].

2 Acoustic metrology

The physical properties of the shockwave field, the basics of shockwave generation and the parameters of the field are well defined in [22] and [23]. In addition to it, the measurements of the field parameters are described by the IEC standard 61846 [12] and are mandatory for regulatory certifications. In contrast to the physical parameters the biological and the bio-molecular effects are not fully understood [11, 18]. It is assumed that the biological effects of ESWT are based on a bio-molecular mechanism and not on the physical-mechanical level [15].

Since the end of the 90th ballistic (also called radial) Extracorporeal Shockwave Therapy sources (rESWT) are on the market and used for the treatments soft-tissue pain situations [7, 17]. In contrast to the focused extracorporeal shockwave therapy (ESWT) devices, the pulses in rEWST are applied manually, guided by patient feedback, without ultrasound or X-ray control. While several reports and clinical studies find good results with rESWT, such as the therapy of chronic plantar fasciitis [8], Tennis elbow [4, 7], some other find no effect [1] or no advantage of rESWT compared to standard procedures [5]. The varying results could be an indication for the influence of clinical-study-conditions and the setting of the hand-piece on the study outcome [2]. This is aggravated by the fact that the physical properties of the acoustic field of rESWT sources are neither fully described nor defined by technical report. Without knowledge on the physical level, predictions on biological effects are difficult to make. To our knowledge, except our recent publications (see [24–26] and [27]) only one publication cover the acoustic field of a rESWT source (see [3]).

Regulatory measurements for the certification process are mostly performed according to the IEC standard 61846 [12]. The IEC standard 61846 was published in 1998, defining the measurement parameters of focused shock-wave fields. Since then the approval of newly designed lithotripters for clinical use are based on the measurement methods described in this standard. Although the standard was written for lithotripters, it is also used to describe otherfocused ESWT devices [22].

For the characterization of the acoustic pressure field of a source several approaches can be used. In [26] a dry test bench using an accelerometer and in [13] and [6] an interferometric approach is suggested. The disadvantage of these methods is that field measurements are difficult to achieve. Acoustic under water measurements are the best option for the evaluation of the field parameters, but also very challenging. Under water measurements need complex and costly experimental setups and with the large amount of different applicators these measurements could be very time consuming.

The aim of our investigation is to characterize the acoustic field of different rESWT sources and make statements on the applicability of the IEC standard 61846 for the measurements of ballistic pressure pulse sources. In order to characterize the device, field mapping is performed on several radial pressure pulse sources using a polyvinylidenfluorid (PVDF) piezoelectric hydrophone.

3 Experimental setup

The measurements are done in a water-tank (LxWxH = 0.8 mx0.8 mx0.4 m) filled with degased (O₂ conzentration < 0.9 mg/L), deionized and 0.2 μm filtered water at 25°C ± 1°C. The hand-piece is mounted directly at the bottom of the water-tank without a membrane between the applicator and the liquid. To ensure a fixed position of the applicator relative to the probe the inertial motion of the applicator is prevented by rigid fixation of the hand-piece to the setup. The hydrophones are moved by custom built 3D positioning system controlled by LabView^© (National Instruments) and program. The hand-piece with 15 mm applicator, which is to our knowledge the clinically mostly used type, is used for the measurements and modeled for the simulations. The hand-piece generator is connected to a pressurized air source (6 Bar), filtered by a 5 μm sinter-bronze air-filter. Several measurement protocols, with single pulse and pulse repetition frequencies (PRF) between 1 HZ and 20 HZ are performed. The setup is shown in Fig. 1. A Polyvinylidene fluoride (PVDF) piezoelectric hydrophone HGL200 (Onda Corp. Sunnyvale – USA) with an active diameter of (200 μm) is used for acoustic measurements. The calibration of the hydrophone is given for the range 1 MHz − 20MHz. A preamplifier AH2010 (Onda corp. Sunnyvale – USA) with +20 dB is attached ro the hydrophone. A HAMEG 1508-2 oscilloscope (HAMEG Instruments GmbH, Germany) is used for signal acquisition. The signal processing is performed in Matlab^© (Math Works Inc.) and Excel^©. Due to an agreement with the manufactures the different hand-pieces of the different manufactures are labeled ashand-piece 1 (HP1) etc.

Figure 1

The measurement setup with the hand-piece attached below a water tank.

Figure 2

Typical pressure-time curve (HP1) measured using a PVDF Hydrophone in degased and deionized water at 25°C at maximum hand-piece setting (4 Bar).

Figure 3

Left Fig.: The inertial oscillations of the applicator (HP2) lead to pressure pulses, which arrive some ms after the initial pulse (at timet = 0). Middle Fig.: Lateral Maximum- and Minimum-pressure distribution 1 mm distance to the source (HP2). Right Figure: Energy-flux-density distribution along the propagation axis (z-axis). Measurements done using a PVDF Hydrophone in degased and deionized water at 25°C. The black solid line depicts a 1/z² fit.

4 Measurement results

A typical pressure time curve of an ballistic pressure pulse source consists of a first positive pressure peak, ranging from 5 MPa up to 20 MPa, mostly followed by a rarefactional phase of about 5 MPa and several oscillations which occur due to stress wave reflections inside the applicator (Fig. 2).

The rise time of the pressure pulse of all hand-pieces are in the range of several microseconds and thus can not be described asshockwaves, which are defined to have a rise time of about some nanoseconds. The inertial motion of the applicator leads to low frequency oscillations of some milliseconds cycle duration, which arrive depending on the applicator and hand-piece several milliseconds after the initial pulse (Fig. 3 left).

Due to the late arrival of the inertial oscillations, these pressure pulses are rarely observed in measurements according the IEC standard, which provide an acquisition time of several microseconds. These pulses are not taken into account in the energy calculations. And to our knowledge there is no clinical investigation on the influence of these motions on biological tissue.

Changing the applicator leads to relatively small differences in the signal shape but could have a big influence on the pressure amplitude. For the same hand-piec (HP5) we observe a pressure change from 7 MPa to 20 MPa, by changing the applicator. The interesting observation we noticed is the huge difference between the pressure-time signals-shape from the hand-pieces of different manufactures, while using the same energy settings and applicator type: As for instance The pressure amplitude is almost two times higher with HP3 while the energy is approximately 40% higher for HP4.

As expected from the theory of a piston source [14], we find a Gaussian distribution for the energy values along the lateral axis (Fig. 3 middle). The energy flux density values along the propagation axis show a 1/z² distribution (Fig. 2 right), which is contrary to the 1/z³ assumptions in recent publications (see [9]). Furthermore we find several publication describing almost no energy afterz = 3 - 5 mm (e.g. [10, 16]), which is not consistent to our measurements, even if we take a 3 medium analysis to model biological tissue.

5 Results and discussion

Our investigation shows that the current standard is not appropriate for the measurement of ballistic sources. Firstly in accordance to the theory of a point source, our measurements show a radial diffusing field for a ballistic sources, which is contrary to the IEC standards intention of focused fields. Consequently the measurement of focused field parameters as described by the standard are not possible. Furthermore, as shown in Fig. 2 the pressure signal is, in contrast to transient lithotripter pressure-pulses, strongly oscillatory making it difficult to define the integration limits for positive and total-energy calculations. Without any specifications on the integration limits, total energy values can be calculated for arbitrary amount of oscillations, and by this the total energy output of a hand-piece can be artificially increased. As for instance, in our measurements we find several manufacture specifications for the energy values that we could not be achieved if we take only the first oscillations into account.

An important observation we noticed is that, although the hand-piece load is given as pressurized air values (in Bar) for all devices we used, the same load for different hand-pieces – even from the same manufacture – lead to different acoustic pressure and energy outputs. This is also the case for the same hand-piece with different applicator. Consequently the applied load can not be used to characterize or compare the applied energy in different studies. However we find a linear relationship between the hand-piece load and the acoustic output of the device. Shock-wave formation could not be observed regardless of the hand-piece or load settings.

The acoustic measurements in water turned out to be very challenging due to the high probability of cavitation, which leads to signal distortion and could destroy the hydrophone. Our aim for the future work is to find an alternative way to characterize the sound field of the source by interferometric measurements with subsequent spatial impulse response simulations.