Figure 36.1
Pressure curve of a shock wave with a short duration (<10 μs) consisting of a compressive phase (peak pressure 30–100 MPa) followed by a tensile phase
Mechanism and Theories of Stone Fragmentation
Initial fragmentation represents a process whereby cracks form as a result of stresses generated by shock waves [1]. Further disintegration occurs due to growth and coalescence of these cracks under repetitive loading and unloading [8]. Beside established mechanisms describing initial fragmentation like tear and shear forces [1], spallation [9], cavitation [10], and quasi-static squeezing [11], further insight was gained by studies of Sapozhnikov [12] introducing the concept of dynamic squeezing (Table 36.1).
Table 36.1
Summary of existing theories for stone fragmentation
Hypothesis | Mechanism | Prerequisites | Type of action | Comments |
|---|---|---|---|---|
Tear and shear forces [1] | Pressure gradients due to impedance changes at stone front and distal surface with pressure inversion | Shock wave smaller in space extension than stone | Hammer-like action Resulting to a crater-like fragmentation at both ends of stone | Only relevant for small focus |
Spallation [9] | Reflected tensile wave at distal surface of with maximum tension at distal part of stone | Shock wave smaller in space extension than stone | Breaking of stone from inside like freezing of water in brittle material | Only relevant for small focus No explanation for stone breakage at front side |
Quasi-static squeezing [11] | Pressure gradient between circumferential and longitudinal waves result to squeezing of stone | Shock wave is broader than the stone SW-velocity is lower in water than in stone | Nutcracker-like action requiring large focal diameters | Only relevant for large focal zone |
Cavitation [10] | Negative pressure waves induce collapsing cavitation bubble at stone surface | Low viscosity of surrounding medium | Microexplosive erosion at proximal and distal end of stone | More important during stone comminution Useful to improve efficiency of shock waves (i.e. EHL) |
Dynamic squeezing [12] | Shear wave initiated at the corner of stone are reinforced by squeezing waves along the calculus | Parallel travelling of longitudinal waves SW-velocity is lower in water than in stone | Nutcracker-like action in combination with spalling | Best theory to explain results of numerical model |
Tear and Shear Forces
If pulse length is smaller than the stone, then the compressive phase of the shock wave will generate pressure gradients, which can result in shear and tensile stresses in the stone. These stresses can produce tearing and shearing to fragment that stone [1]. In this theory, also the shock wave reflection at the stone-water interface with pressure inversion and splitting off stone material by tensile stress of the reflected wave is emphasized (Fig. 36.2a).
Figure 36.2
Different theories for initial stone fragmentation. (a) Tear and shear forces: Shock waves are transmitted and reflected at the low impedance stone-water interfaces with pressure inversion splitting off stone material by tensile stress. (b) Spalling: Distal stone surface as acoustically soft interface generates a reflected tensile wave of the initially compressive longitudinal SW-pulse propagating through calculus with maximum tension within the distal third of the stone (high-speed shadow-graphy by Zhong). (c) Quasi-static squeezing: Breakage of stone by tensile stress of the circumferential shock wave due to lower SW-velocity in surrounding fluid than within the stone (Modified from Eisenmenger). (d) Cavitation: Negative pressure waves of high-speed shocks cause cavitation in liquids surrounding stones and within microcracks or cleavage interfaces by inducing microjets. (e) Dynamic squeezing: Shear waves initiated at the corners of the stone and driven by squeezing waves along the calculus lead to greatest stress and tension (3D computer simulation according to numerical model by Cleveland). Note different pressure distributions and traveling time of waves inside and along stone surface. Blue = compressive phase, Green = maximum shear stress (55 MPa), Red = maximum tensile stress (80 MPa)
Spallation
The fluid at the posterior stone surface represents an acoustically soft interface, and the leading compressive phase will be reflected as a tensile wave. The amplitude of the tensile stress depends on the difference in acoustic impedance and the geometry of the stone surface. Using high-speed imaging to show stress waves in a translucent test stone (Fig. 36.2b), maximum pressure occurred within the distal part resulting in a fracture about 1/3 from distal end [9]. This fracture mechanism is considered similar to freezing of water inside brittle material.
Quasi-Static Squeezing
If the focal zone is broader than the stone pressure waves travel in the fluid along the surface. The leading compressive phase can create circumferential stress, which acts on the stone by quasi-static squeezing inducing a binary fragmentation similar to a nutcracker with first cleavage surfaces parallel or perpendicular to the axis of SW-propagation (Fig. 36.2c). This assumes that the SW-velocity in surrounding fluid is much lower than elastic velocities within the stone. The longitudinal SW moves through the stone leaving the thin waves in the fluid encircling and squeezing the stone [11]. For squeezing to be effective the focal width of the lithotripter must be wider than the stone, thus high fragmentation efficiency will be promoted by large focal diameters (i.e. up to 20 mm). Data suggest that P+ could be reduced to 10–30 MPa, sufficient to overcome fracture thresholds. This hypothesis has stimulated discussions about the importance of larger focal size and lower pressure compared to small focal size with high pressure in large-aperture sources.
Cavitation
Cavitation generated by the negative pressure phase of shock waves occurs in the fluid surrounding stones and within microcracks or cleavage interfaces (Fig. 36.2d). For initial fragmentation, cavitation is less relevant, but becomes important as stone fragments become smaller. Cavitation-induced erosion is especially observed at anterior surface of stones [10]. Suppression of cavitation using highly viscous media or hyperpressure or overpressure significantly reduces disintegrative SW-efficacy [13]. Recognition of the role of cavitation in stone comminution has led to efforts to enhance the action of cavitation bubbles such as tandem shock waves generated using a piezoelectric source fitted to an electrohydraulic system with an additional discharge circuit to produce the second pulse [14]. The same has been realized recently by the use of high intensity focused ultrasound with and without an electrohydraulic lithotripter [15]. However, cavitation can be also detrimental to fragmentation as it results in production of gas bubbles lasting for many seconds therefore attenuating subsequent impulses [16]. Higher PRF results in more cavitation bubbles, while higher acoustic energy leads to a longer lifespan of the cavitation bubbles.
Dynamic Squeezing
This theory mainly combines spallation and quasi-static squeezing. Following predictions from a numerical model Sapozhnikov presented experimental evidence of dynamic squeezing [12, 17] demonstrating that shear waves initiated at the corners of the stone and driven by squeezing waves along the calculus lead to greatest stress, whereas reflection of longitudinal waves at posterior surface was less important. Thus, in dynamic squeezing calculi are fragmented by shear waves created inside the stone reinforced by squeezing waves from the lateral stone borders (Fig. 36.2e).
Dynamic Fatigue
Fragmentation inflicted by SWL accumulates during course of treatment, leading to eventual destruction of stone integrity [8]. Therefore, stone comminution is characterized as a progressive process consisting of initiation (based on dynamic squeezing), propagation (associated by cavitation), and coalescence (due to increasing fragility). Finally, mechanical stresses produce micro-cracks resulting in a sudden break-off of calculus once its molecular structure is destroyed. This theory relates physical stone properties (fracture toughness, acoustic speed, density, void dimensions) to SW-parameters (peak pressure, pulse width, pulse profile).
Relevance of Different Theories of Stone Fragmentation
Sapozhnikov [12] carried out a set of experiments testing multiple mechanisms on a research lithotripter: spalling, quasi-static squeezing, and cavitation (Table 36.2). Whereas only one experiment supported spalling and quasi-static squeezing, dynamic squeezing sufficiently described initial fragmentation in all experiments (Fig. 36.3). Tear and shear forces and spallation remain only relevant in small focal sizes. The current consensus is that focal width may have a critical role in stone breakage at least for initial fragmentation.
Table 36.2
Models and results of experimental evaluation of stone fragmentation by shock waves
Mechanism | Model | Hypothesis | Stone model/numerical calculation |
|---|---|---|---|
Spallation | Stone length 8–18 mm | Stone fractures at same distance from the distal end | Stone fractures at 1/3 from the distal end dependent from length |
Block of prox. surface by corprene disk | Stone fracture is significantly inhibited | Only little difference (50 vs 45 SW) Pressure field similar at last 1/3 | |
Squeezing | Baffle ringing proximal end | Stone fracture is significantly inhibited | Significant inhibition (300 vs 45 SW) But reduced stress field still at last 1/3 |
Conical shape of stone front | Stone fracture is not inhibited | Significant inhibition (200 vs 45 SW) Pressure field reduced due to diffraction | |
Block of prox. End (complete) | Stone fracture is not inhibited | Significant inhibition (212 vs 45 SW) Pressure field reduced due to absorption |
Fig. 36.3
Stress fields in the different stone experiments using a research lithotripter patterned after Dornier HM3 (Sapozhnikov et al. [12]). The maximal stress field (a) is little changed by blocking the longitudinal wave entering the stone (e) or altering the distal end of the stone (b, c, g). However, blocking the circumferential squeezing wave alone (d) or preventing the creation of shear waves at the corners (f, h) significantly reduces the intensity of stress
Based on this, recent broad-focus, low-pressure lithotripters (LithoSpace, LithoGold, XX-ES) attracted attention as research showed that focal width affects stone breakage in several ways [7, 18–21]. In vitro, the disintegrative efficiency of XX-ES was superior to HM3 (634 vs. 831 SW) and similar to that of the Siemens Lithoskop (Table 36.3). Since no data of applied energy at different shock wave sources were provided, differences in configuration and acoustic output of both devices must be considered when interpreting results. Moreover, recently modification of the lens of the electromagnetic System-C of Siemens resulted in a larger focal size and in-vitro-efficiency [22].
Table 36.3
Extracorporeal shockwave lithotripsy
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