Shock wave therapy is an innovative, non-invasive, and effective treatment method with a wide range of applications in the medical field. First used by Dr. Christian Chaussy in 1980 to break kidney stones, shock waves are now employed in various fields, including orthopedics, urology, neurology, cardiology, sports medicine, dermatology, and aesthetics.

The treatment involves the delivery of high-energy acoustic waves from outside the body to the targeted area. Shock waves are categorized into two main types: focused and radial. Focused shock waves have high energy density and can penetrate deep tissues, while radial pressure waves provide more superficial effects. Both types are used for different purposes, depending on the condition being treated.

Focused shock waves are a therapeutic method that involves the penetration of high-energy acoustic waves into deep tissues by focusing on a specific point. These waves are characterized by high positive pressure amplitudes and sudden pressure increases. Shock waves transmit energy from the point of production to the target area, promoting tissue regeneration and healing.

Focused shock waves are widely used in fields such as orthopedics, urology, and sports medicine. They are effective in treating conditions such as chronic tendinopathy, plantar fasciitis, stress fractures, and calcific tendinitis. In urology, this therapy is successfully applied in the treatment of conditions such as erectile dysfunction, Peyronie's disease, and chronic prostatitis. This treatment method alleviates pain, promotes tissue regeneration, and supports functional recovery. Additionally, it offers a less invasive alternative to surgery, shortening the recovery period.

The biomechanical effects of shock waves include increased microcirculation at the cellular level, regulation of the inflammatory response, and stimulation of collagen production. These effects accelerate tissue regeneration and reduce pain. When applied correctly, focused shock waves are considered a safe and effective treatment option, offering patients an improved quality of life.

The purpose of this study is to characterize the shock waves produced by the Modus Focused Device and to determine the energy (mj) obtained at the tip of the applicator. This report includes only one measurement result for the Modus Focused ESWT Device.

2.1. Derived Acoustic Impulse Energy: The spatial integral of the derived impulse intensity integral over a circular cross-sectional area with a radius R that includes the focus in the x-y plane. Symbol/Unit: ER (J)

2.2. Derived Impulse Intensity Integral: The time integral of the instantaneous intensity at a specific point within the pressure pulse field over the pressure pulse waveform. Symbol/Unit: PII (J/m²)

2.3. Shock Wave: Waves characterized by high positive pressure amplitudes and a sharp rise in pressure compared to ambient pressure; these waves propagate through mediums such as water or human tissue.

2.4. Focal Cross-Sectional Area: The area of the peak-positive acoustic pressure contour at the -6 dB level within a plane perpendicular to the beam axis that includes the focus. Symbol/Unit: Af (m²).

2.5. Focal Region: The shortest distance along the z-axis connecting points on the -6 dB contour of peak-positive acoustic pressure in the x-z plane on either side of the focus. Symbol/Unit: fz (m).

2.6. Maximum Focus Width: The maximum width of the -6 dB p+ contour around the focus in the x-y plane. Symbol/Unit: fx (m).

2.7. Orthogonal Focus Width: The maximum width of the -6 dB p+ contour around the focus in the x-y plane perpendicular to fx. Symbol/Unit: fy (m).

2.8. Acoustic Pressure: The ambient pressure at a specific point in the acoustic field at a given moment in time. Symbol/Unit: p (Pa).

2.9. Impedance: A value dependent on the density of the liquid and the speed of sound waves. Symbol/Unit: Z (kg/(m²·s)).

2.10. Peak-Positive Acoustic Pressure: The maximum acoustic pressure at any spatial location within the pressure pulse field. Symbol/Unit: p+ (Pa).

2.11. Test Setup: The arrangement used to characterize the shock wave produced by the Modus Focused Device.

2.12. Treatment Area: The region between the Maximum Pressure Point (Focus) and the boundary where the shock wave effect decreases to 5 MPa.

In the formation of a shock wave, a single positive pressure pulse (p+) is followed by negative tensile pressure pulses (p-). The pressure pulse lasts approximately 1 µs. The focus of the shock wave is the area where the pressure is equal to or greater than 50% of the peak-positive pressure (p+). This area is referred to as the -6 dB focal point (Figure 1). The rise time is defined as the time it takes for the instantaneous acoustic pressure at the focal point to rise from 10% to 90% of the peak-positive acoustic pressure and is denoted as tr (Figure 1). The compression pulse duration is the time interval that begins when the instantaneous acoustic pressure first exceeds 50% of the peak acoustic pressure and ends the next time the instantaneous acoustic pressure reaches this value. It is denoted as tFWHMp+ (Figure 1). This area represents the focal region.

Figure 1: Typical Pressure Pulse Waveform at the Focus

- According to International Standards, the value of +Pmax measured at the z-coordinate, when halved, corresponds to the -6 dB area and is equal to +Pmax/2. The area between +Pmax and +Pmax/2 is referred to as the Focal Area or Focal Region.
- In Figure 2, the red area represents the focal point, which is the high-pressure point of the shock wave.
- The region between the Maximum Pressure Point (Focus) and the boundary where the shock wave effect decreases to 5 MPa is called the Treatment Area. The 5 MPa Treatment Area formed by the propagation of shock waves represents the entire blue and red areas shown in Figure 2.
- The treatment area of the shock wave inside the body is not the same as the cross-sectional area of the -6 dB focal region. The treatment area can be larger than the focal point created by the shock wave. The 5 MPa Treatment Area, a parameter based on blood pressure, is the region where the biological effects of the shock waves are produced (Figure 2).

Figure 2: -6 dB Focal Region & 5 MPa Treatment Area

Measurements are taken at x-y-z coordinates to create a pressure map. As shown in Figure 4, measurements are taken with 0.25 mm movements in the x and y directions, and 0.5 mm sampling intervals in the z direction.

The signal obtained from the oscilloscope is processed and converted into a Pressure-Time graph, and energy calculations are made by integrating the resulting curve.

Figure 4: Sampling Interval

The energy per pulse (mj/mm²) is obtained by deriving the Pressure-Time graph and calculating the area under the curve. As shown in Figure 6, the graph extends into the negative region. In the total energy calculation (Etotal), the effect of negative pressure is also considered, while the unindexed energy calculation or Positive Acoustic Pressure Energy (E+) is obtained by calculating the enclosed area in the positive region of the graph.

Acoustic Pressure Energy is an important parameter in clinical applications. It is assumed that shock waves only have an effect on tissues when certain energy thresholds are exceeded. Energy is determined by integrating the time curve of the pressure wave p(t). It is directly proportional to the Surface Area (A) and inversely proportional to acoustic impedance

- Z; The characteristic acoustic impedance of water.

- P; The acoustic pressure function.

- S; The focal surface in the x-y plane containing the focus, with spatial polar coordinates r and q.

- t; Time

The therapeutic efficacy of the shock wave depends on whether the acoustic energy is distributed over a wide area or focused on a locally confined treatment region (focal region). Energy flux density (EFD+) is obtained by calculating the energy per unit area (E/A). Its unit is mj/mm².

This integral calculation is derived from the double integral provided in the relevant standard.

The **Derived Focal Acoustic Impulse Energy (Ef)** is the spatial integral of the derived impulse intensity integral over a circular cross-sectional area with a radius R in the x-y plane, which includes the focal point. Its unit is Joules (J).

PII(r) is the derived impulse intensity integral at a radial distance r. It represents the time integral of the instantaneous intensity at a specific point during the pressure pulse. Its unit is J/m². It is calculated as follows:

The boundary range (r=0,r=R) is applied and then re-derived.

Figure 7: Pressure (y-axis) and Time (x-axis) Measurements of a Shock Wave

Maximum positive pressure (p+) is the highest pressure amplitude of the shock wave. The -6 dB pulse width is the interval during which the pressure remains higher than 50% of p+. The signal obtained from the oscilloscope is converted into a pressure graph, and the area under the pressure graph will indicate the energy result. This calculation yields the energy flux density (EFD+) in mj/mm².

In the Modus Focused ESWT device, the energy flux density is 0.11 mj/mm², and the Positive Acoustic Pressure Energy (E+) is 1.38 mj. As is known, each energy transferred to the tissue accumulates to form Etotal. Higher energy can be obtained by increasing the number of pulses. If 2400 pulses are assumed to be applied with the Modus Focused ESWT device, 3.31 J can be obtained by using the formula:

• Modus Focused ESWT cihazında enerji akıs yogunlugu : 0,1056 mj/mm2’dir. Pozitif Akustik Basınç Enerjisi (E+) ise 1,38 mj’dür.

Number of Pulses×E (mj)/1000(J)=3.31J

However, the size of the focal region does not change as energy increases. The size of the focal region depends on factors such as the geometric shape of the reflector and the position of the electrode.

Table 1: Measurements Taken in the +x Direction at 0.25 mm Sampling Intervals on the z-Coordinate Plane at the 37.33 MPa Point

Measurements taken from the 37.33 MPa point indicate that the focal region is approximately 4 mm, while the treatment area is approximately 12 mm.

Table 2: Measurements Taken in the -z Direction on the z-Coordinate at the 42.16 MPa Point

The penetration depth of the İnceler Modus Focused ESWT device has been measured at 84.5 mm.

Modus Focused Device -6 dB Focal Width at 37.33 MPa Focus Point:

• P+ : 37,33 Mpa

• fx(-6 dB) : 4 mm

• fy(-6 dB) : 4 mm

• fz(-6 dB) : 28,5 mm

• fx,y( 5 Mpa) : 12 mm (Treatment Area – 5 Mpa)

• EFD+ : 0,11 mj/mm2

The measured value from the Modus Focused ESWT device is observed to be within the appropriate range as referenced in the literature.

According to a previous study (Chow, I.H.; Cheing, G.L. Comparison of different energy densities of extracorporeal shock wave therapy (ESWT) for the management of chronic heel pain. Clin. Rehabil. 2007), regardless of the type of shock wave generators, ESWT devices can be classified as follows:

• Low Energy Density: Energy flux density < 0.1 mJ/mm²

• Medium Energy Density: Energy flux density between 0.1–0.2 mJ/mm²

• High Energy Density: Energy flux density > 0.2 mJ/mm²

EFD (Energy Flux Density) is a parameter used by professionals in clinical practice to indicate the energy flow perpendicular to the propagation direction of shock waves across the treated area. Therefore, ESWT can be categorized into low (<0.08 mJ/mm²), medium (0.08–0.28 mJ/mm²), and high (up to 0.60 mJ/mm²) intensities, which may lead to different clinical applications.

Although there is no sharp distinction in the literature, it is commonly understood that the İnceler Medikal - Modus Focused ESWT Device has a medium energy flux density. It is not intended for lithotripsy but is suitable for use in conditions such as physical therapy and tissue regeneration. By adjusting the step value on the Modus Focused ESWT device, lower power levels can be achieved, allowing it to be used in various clinical applications. Therefore, low energy flow can also be obtained with the Modus Focused ESWT Device.