Debate on momentum transfer in shock wave therapy and neurostimulation – reply to Mohana Sundaram et al.: correspondence

Dear Editor, We got notice from the below referred correspondence of Mohana Sundaram et al: Mohana Sundaram A, Ezebialu CO, Mofatteh M, Emran TB. Recontextualizing momentum transfer in shock wave therapy—insights into neurostimulation and beyond: correspondence. Int J Surg. 20 August 2025. doi: 10.1097/JS9.0000000000003236. Epub ahead of print. PMID: 40839066[1]. This correspondence comments on our article. The interaction of shock waves with biological tissue – momentum transfer, the key for tissue stimulation and fragmentation 1 April 2025:11(4):2810-8[2]. The correspondence of Mohana Sundaram et al presents some “key gaps” and critical comments on the concept of momentum transfer as key physical factor in shock wave therapy. Our response is as follows: Mohana Sundaram et al criticize our paper with six comments: 1. Most of the hypothetical mechanisms of action are speculative and lack robust evidence. 2. Significant research is overlooked. 3. Only mechanotransduction is discussed, while other pivotal mechanisms have not been discussed. 4. Cavitation, another mechanism, not mentioned. 5. Neglecting adaptive response of the body. 6. Predominantly citation of proprietary devices. We have responded to critics 1–6 after a brief review of the content of our paper. The first part of our reply clarifies the substance of the paper with the restriction on physical aspects of shock waves, providing appropriate forces acting on biological subjects: There is nothing but mechanical input to biological tissue. All of what happens in succession is due to inherent biological or biochemical mechanisms that may be triggered by adequate mechanical stimuli. The exciting wide field of growing biological responses involves biological and biochemical processes initiated by forces via mechanotransduction. Our paper: “The interaction of shock waves with biological tissue—momentum transfer, the key for tissue stimulation and fragmentation 1 April 2025:11(4):2810-8.”[2] This study relates to the physical mechanism of the interaction of shock waves with biological tissues. It develops a fundamental approach to the physics of forces acting during the application of medical shock waves to specific tissues. The mechanism of momentum transfer elucidates the effect of shock waves on different types of tissues in a far-reaching manner. Momentum transfer, following the reflection of shock waves at the acoustic interfaces of different organs, generates appropriate forces for stimulation and fragmentation. This is the key message of the first part of this study. In more detail, the parameter energy flux density is widely used to characterize and differentiate shock waves, giving an impression of the strength of a shock wave. However, this parameter does not directly correlate with medical efficiency. Even though shock waves have been used in medicine since 1980, their mechanism of action is not completely understood. Notably, which shock wave parameter is decisive? Is it the pressure, energy, energy flux density, rise time of the pressure, negative slope of pressure curve or something else? The parameter momentum of a shock wave was unnoticed for a long time and brought to attention in our paper[3]: Wess, Fragmentation of brittle material by shock wave lithotripsy. Momentum transfer and inertia: A novel view of fragmentation mechanisms. Urolithiasis 48, 137–149 (2020).https://doi.org/10.1007/s00240-018-1102-6 This shock wave parameter offers the opportunity to elucidate the working mechanism of the shock waves. Shock waves are mechanical waves governed by Newton’s laws of motion. However, direct chemical, biological, or other healing effects cannot be expected. They are no ionizing waves, X-rays, or electromagnetic waves, but purely mechanical waves. There are no chemical or biological characteristics hidden in the mechanics of shock waves. Nevertheless, a growing number of biological effects in living tissues, cascades of biochemical processes, and plasticity of synaptic connections seem to be triggered by shock waves. However, this astonishing wide spectrum of medical shock wave applications cannot be explained by the individual features of the shock waves for individual medical indications. This requires a comprehensive mechanism for a wide variety of applications. We consider mechanical forces as an indispensable requirement for the interaction of shock waves with living tissues. The widely used parameter energy flux density, ED, does not determine the efficiency of the shock wave. High-energetic shock waves may pass through homogeneous tissue without affecting the tissue unless inhomogeneities cause reflections at interfaces with different acoustic impedances. The first essential part of our study deals with the mechanism of momentum transfer, which provides the basis for the generation of forces. Forces are decisive factors acting on living tissues. The key point of our study is to recognize the momentum of shock waves and their transfer to specific tissue structures by reflection. A force is not generated until the shock wave momentum is reflected according to the tissue-specific reflection coefficient, a force is generated. The force is determined and can be calculated using Newton’s laws of motion (conservation of momentum, one of the basic columns of classic physics). The forces generated by reflection act on tissues and stones in various ways. They can generate pressure, tension, and shear waves. As shown in Figures 1 and 2, the shock waves feature a positive and smaller negative momentum (see Figs 1 and 2). Depending on the sign of the reflection coefficient, the generated forces may be either positive or negative (pressure and tension). In the case of solid materials (stones), several pressure and shear waves may be generated, which change the polarity at the rear surface of the stones. This is the basis of Hopkinson`s effect which is an important factor in stone fragmentation. Figure 1.: Typical pressure values measured on the axis of the shock wave propagation. The shock wave travels from right to left, starts with a rapid rise within a few nanoseconds and declines to zero in approximately 1 microsecond, followed by a tensile pressure of several microseconds.Figure 2.: According to the positive part of the pressure curve, a momentum in the propagation direction of the shock wave (to the left) is generated followed, due to tensile pressures, by momentum to the opposite direction (to the right). Further decaying reverberations follow with alternating directions. Notably, these and other effects are consequences of the forces generated by momentum transfer and are not independent additional mechanisms. These forces can initiate or trigger further biochemical processes via mechanotransduction and mechanosensory transduction. Owing to their wave character, shock waves can be focused and applied in selective tissue areas in the body of patients. Using the mechanism of momentum transfer, we introduce a new theory to elucidate the mechanism of generating adequate forces for fragmentation and stimulation. These forces trigger multiple biological processes and activate the inherent healing mechanisms. They do not modulate synaptic plasticity directly but as hypothesized, by frequent and robust stimulation of nerve cells. However, this study did not cover a complete number of biological and medical applications. The cited examples are selected for demonstration. We do not claim that all the effects of shock waves are based on momentum transfer; however, we suppose that a wide spectrum of medical shock wave applications is covered by this mechanism, probably including inflammatory signaling. Shock waves are not always effective; however, if they are effective, the primary cause is the ruled physical feature of the shock wave. We must emphasize that shock waves affect tissues exclusively in a mechanical manner. There were no genuine biological or chemical interactions. All subsequent biological effects are due to the mechanics of shock waves, particularly forces. To date, shock waves can only deliver an adequate mechanical trigger to initiate the following biochemical processes, including the stimulation of nerve cells, which may in turn lead to the modification of synaptic plasticity. The remarkable number of different medical shock wave applications and the complexity of the triggered cascades, etc. – if appear – do not have a separate individual and pivotal mechanism hidden in shock waves. We agree that cavitation is another mechanism that is considered responsible for certain effects of shock waves, such as enhancing drug delivery across the blood–brain barrier. Cavitation, however, requires a closer look, as it is, in many cases, an unwanted side effect causing tissue lesions and significant shielding of shock wave energy. In Figure 2, the positive peak gives rise to a positive momentum in the propagation direction of the shock wave (to the left), whereas the negative (tensile) part of the curve gives rise to a smaller negative momentum to the right (against the propagation direction of the shock wave). Cavitation bubbles are generated by shock waves under specific conditions. The negative slope of the pressure curve (see Fig. 2) can tear the water and create cavitation bubbles if the tensile stress surpasses the cavitation threshold and cavitation nuclei are present. These bubbles are typically stationary. They grow within a few microseconds and collapse within a millisecond, while radiating a secondary spherical shock wave. The radius of the secondary shock wave is a measure of the time elapsed after the bubble collapses. All the phases of the process (generation, growth, collapse, and radiation of secondary shock waves) are shown in Figure 3. Figure 3.: Shock wave pulse visualized by color Schlieren optics. Shock waves are pressure waves traveling, for example, through water as pressure distortions with a velocity of app. 1500 m/s. Usually, the pressure distortions are not visible to the naked eye. A color optical Schlieren apparatus (see Wess and Mayer[ 3 ]) can visualize gradients of the pressure distortions, which are here displayed in red (pressure rise) and in green (pressure decline). The shock wave is traveling from right to left. The first small red triangle on the symmetry axis left depicts the area of rapid pressure rise. From the peak, the pressure decreases, displayed in green color until the minimum pressure is reached and is again rising (displayed in red). Several smaller reverberations with alternating pressures and according to pressure gradients are displayed further to the right. After the first minimum pressure (right rim of the first green line), a field of cavitation bubbles occurs. Some of the bubbles collapse already and radiate secondary spherical shock waves depicted as the circles at the right side of the frame. Shock waves like the one displayed are transmitted from outside the body through the intact skin into deeper target areas of the tissue, where they stimulate tissue interfaces or fragment body stones via the mechanism of momentum transfer. Only a few bubbles develop microjets when close to surface inhomogeneities (e.g., surfaces of organs). Notably, most of the experiments were performed in degassed water and not in human tissue. Most medical applications (apart from high-intensity fragmentation of stones) are in a low-energy range to avoid cavitation because of the risk of tissue lesions due to puncture of small blood vessels. In the case of neurostimulation, the shock power is strictly limited to a level below the possible cavitation. Even in stone fragmentation, cavitation is not the primary but a secondary effect that might help to further fine fragmentation of primary coarse fragments owing to the direct application of forces generated by momentum transfer. The cited papers Pishchalnikov Y et al[4] and Schelling et al[5], deal with gas bubbles generated by rapid shock wave pulses in saturated water that last much longer (~100 ms or longer). These conditions are not suitable for clinical applications. Streaming, which refers to the flow of bubbles, can occur in saturated water but not in solid tissue. With the exemption of liquids (blood, urine, etc.), cavitation is stationary if present in the tissue. Schelling et al[5] used gas bubbles on isolated frog nerves lasting longer than seconds and exposed them to shock waves. They concluded that cavitation was the mechanism of shock wave stimulation. Apart from the fact that they used long-lasting gas bubbles rather than short-duration cavitation bubbles (less than 1 millisecond) created by shock waves, this statement is not exclusive. This shows that in this special experiment, shock waves can stimulate nerve cells, but this is not the only way to stimulate nerve cells. There are many mechanisms known to stimulate nerve cells (electric or mechanical). An essential result of our study is that shock waves stimulate nerve cells via momentum transfer, which transforms a microsecond pulse of the original shock wave (not an adequate stimulation pulse) into a millisecond pulse, which is considered an adequate pulse for nerve stimulation. This is different from diagnostic ultrasound, which usually does not stimulate nerve cells. There is no need to increase the shock wave energy beyond the cavitation level of the tissue to stimulate nerve cells. Shock waves can stimulate nerve cells without causing cavitation. Cavitation is no contradiction to the mechanism of momentum transfer. The second part of the paper deals with possible deductions from the findings, particularly the mechanism of neural stimulation. This is clearly hypothetic. We developed an ambitioned hypothesis of neurostimulation by shock waves, including the modification of memory structures in the brain. It is motivated by observations, such as repetitive applications that strengthen the success of a treatment, such as learning, and by the selection of the point of highest pain perception for efficient result of the application. The momentum transfer mechanism transforms microsecond pulses into millisecond pulses (see the original paper), which enables adequate nerve stimulation (unlike ultrasound). The impact of peripheral and central nerve stimulation may be reasonable in areas of shock wave applications, such as pain therapy. The motivation and justification for publishing such a hypothesis are based on scientific practice. The method of science (Popper) According to the philosophy of science of Karl Popper (1902–1995) in his book The Logic of Scientific Discovery (1959), a translation of Logik der Forschung (1934) hypotheses and scientific theories[5] cannot verified but may be falsified by contradictory observations[6]. If a scientific hypothesis delivers reliable predictions, it may be a valuable tool. Otherwise, the hypothesis must be modified or replaced by a better one. According to Karl Popper, the scientific goal is to falsify a hypothesis or its aspects and replace it with a better one. We welcome everyone to join us to try to falsify our hypothesis, develop a better hypothesis, and test it. Ham et al[7] developed focused shock wave therapy to stimulate deep brain regions without surgery, published online 30 August 2024. However, our paper was submitted before 24 April 2024. The paper by Ham et al can be considered as an independent, excellent support of our hypothesis. They showed that shock waves can stimulate deep brain regions by affecting memory and cognitive functions. They used an “optimized” pressure profile with a time-varying pressure gradient. There was no contradiction in our findings. Different shock waves with different pressure profiles (different time durations, peak pressures, rise times, and pressure gradients) result in different momentums. The forces generated by the reflection and momentum transfer differ and affect the tissue differently. This hypothesis is open for discussion. Answers for the comments 1–6: 1. Most of the hypothetical mechanisms of action are speculative and lack robust evidence Answer: The hypothesis is based on various observations such as stimulation of nerve cells by shock waves, hyperstimulation alleviating pain sensation, etc. (see: Wess O. A neural model for chronic pain and pain relief by extracorporeal shock wave treatment. Urol Res. 2008; 36:327-34). In addition to surgery, the application of shock waves usually requires several repeated applications, assuming that learning and training mechanisms are involved. Additionally, Ham et al[7] supported this hypothesis. Our hypothesis may be new and demanding but not unreasonable. However, this hypothesis may be falsified (Popper). 2. Significant research is overlooked Answer: This paper primarily deals with the physics of momentum transfer in shock wave therapy. We are not aware of any related publications that are not listed in the references. Publications dealing with medical, biological and biochemical issues (instead of technical issus) are not subject of our paper. 3. Only mechanotransduction is discussed, while other pivotal mechanisms have not been discussed. Answer: With the exeption of the mechanism of cavitation (see below), we are not aware of other pivotal mechanisms of shock waves in medicine. Which pivotal mechanisms are missing? 4. Cavitation, another mechanism, is not mentioned Answer: Cavitation is a mechanism that occurs in high-energy shock waves and is usually unwanted because it may (if at all) generate tissue lesions. Most of the relevant applications (exemption stone fragmentation) of cavitation do not play a dominant role (see, e.g., Ham et al) 5. Neglecting adaptive response of the body Answer: This is a biological subject and not a physical subject in our paper. 6. Predominantly citation of proprietary devices Answer: Transcranial pulse stimulation is a relatively new method (other than ultrasound, electric, etc.). Currently, the only commercial device for human application is NEUROLITH®, developed by Storz Medical in cooperation with the University of Vienna. It is not surprising that most of the published papers are based on this device and the people involved.