Colombeau's theory and shock wave solutions for systems of PDEs

In this article we study the existence of shock wave solutions for systems of partial differential equations of hydrodynamics with viscosity in one space dimension in the context of Colombeau's theory of generalized functions. This study uses the equality in the strict sense and the association of generalized functions (that is the weak equality). The shock wave solutions are given in terms of generalized functions that have the classical Heaviside step function as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function that have to satisfy part of the equations in the strict sense and part of the equations in the sense of association.

Ultrastructural and immunocytochemical evaluation of the effects of extracorporeal shock wave treatment in the hind limbs of horses with experimentally induced suspensory ligament desmitis

Objective-To evaluate the effects of extracorporeal shock wave therapy (ESWT) on affected ligaments in the hind limbs of horses with experimentally induced suspensory ligament desmitis by use of ultrasonographic, ultrastructural, and immunocytochemical techniques.Animals-10 horses.Procedure-Suspensory ligament desmitis was induced in both hind limbs of each horse by use of 2 collagenase injections (administered 2 weeks apart) in each suspensory ligament. Two weeks after the second injection, the right hind limb of each horse was treated with ESWT (3 treatments at 3-week intervals)- the left hind limb was not treated (control limb). Periodically during the study, the healing process was monitored ultrasonographically and the proportions of ligaments affected with lesions were assessed. Four weeks after the last ESWT treatment, biopsy specimens were collected from all ligaments for ultrastructural evaluation and immunocytochemical analysis of transforming growth factor beta-1.Results-The difference in the proportion of the lesion-affected ligament between ESWT-treated and control limbs was significant (P < 0.05) from 3 weeks after the second ESWT treatment to the end of the study. Compared with control ligaments, ESWT-treated ligaments had more small, newly formed collagen fibrils and greater expression of transforming growth factor beta-1 4 weeks after the last ESWT treatment was administered.Conclusions and Clinical Relevance-Results have indicated that ESWT appears to facilitate the healing process in horses with experimentally induced hind limb suspensory ligament desmitis.

Microvascular response to shock wave application in striated skin muscle

This study aims to quantify by intravital microscopy the microhemodynamic response after extracorporeal shock wave application (ESWA) to the physiologic microcirculation of the mouse dorsal skinfold chamber.

Radial extracorporeal shock wave therapy (rESWT) induces new bone formation in vivo: results of an animal study in rabbits

The aim of this study was to investigate if radial extracorporeal shock wave therapy (rESWT) induces new bone formation and to study the time course of ESWT-induced osteogenesis. A total of 4000 impulses of radial shock waves (0.16 mJ/mm²) were applied to one hind leg of 13 New Zealand white rabbits with the contralateral side used for control. Treatment was repeated after 7 days. Fluorochrome sequence labeling of new bone formation was performed by subcutaneous injection of tetracycline, calcein green, alizarin red and calcein blue. Animals were sacrificed 2 weeks (n = 4), 4 weeks (n = 4) and 6 weeks (n = 5) after the first rESWT and bone sections were analyzed by fluorescence microscopy. Deposits of fluorochromes were classified and analyzed for significance with the Fisher exact test. rESWT significantly increased new bone formation at all time points over the 6-week study period. Intensity of ossification reached a peak after 4 weeks and declined at the end of the study. New bone formation was significantly higher and persisted longer at the ventral cortex, which was located in the direction to the shock wave device, compared with the dorsal cortex, emphasizing the dose-dependent process of ESWT-induced osteogenesis. No traumata, such as hemorrhage, periosteal detachment or microfractures, were observed by histologic and radiologic assessment. This is the first study demonstrating low-energy radial shock waves to induce new bone formation in vivo. Based on our results, repetition of ESWT in 6-week intervals can be recommended. Application to bone regions at increased fracture risk (e.g., in osteoporosis) are possible clinical indications.

Histomorphologic evaluation of extracorporeal shock wave therapy of the fourth metatarsal bone and the origin of the suspensory ligament in horses without lameness

OBJECTIVE: To determine via histologic examination and scintigraphy the effect of focused extracorporeal shock wave therapy (ESWT) on normal bone and the bone-ligament interface in horses. ANIMALS: 6 horses without lameness. PROCEDURE: Origins of the suspensory ligament at the metacarpus (35-mm probe depth) and fourth metatarsal bone (5-mm probe depth) were treated twice (days 0 and 16) with 2,000 shocks (energy flux density, 0.15 mJ/mm2). One forelimb and 1 hind limb were randomly treated, and the contralateral limbs served as nontreated controls. Bone scans were performed on days -1 (before ESWT), 3, 16, and 19. Histomorphologic studies of control and treated tissues were performed on day 30. RESULTS: ESWT significantly increased the number of osteoblasts but caused no damage to associated soft tissue structures and did not induce cortical microfractures. A significant correlation between osteoblast numbers and radiopharmaceutical uptake was noticed on lateral views of the hind limb on days 3 and 16 and on caudal views of the forelimb on day 3. CONCLUSIONS AND CLINICAL RELEVANCE: Results suggested that ESWT has the potential to increase osteoblast numbers in horses. The correlation between increased osteoblast numbers and radio-pharmaceutical uptake 3 days and 16 days after the first ESWT suggested that stimulation of osteogenesis occurred soon after ESWT. No damage to bone or the bone-ligament interface should occur at the settings used in this study, and ESWT can therefore be administered safely in horses.

Extracorporeal shock wave lithotripsy for distal ureteral calculi: what a powerful machine can achieve

PURPOSE: We assessed the efficacy of extracorporeal shock wave lithotripsy (ESWL, Dornier Medical Systems, Inc., Marietta, Georgia) for distal ureteral calculi with the HM3 (Dornier Medical Systems, Inc.) lithotriptor. MATERIALS AND METHODS: A total of 585 consecutive patients with distal ureteral calculi were treated with ESWL using an unmodified HM3 lithotriptor. Of these patients 67 referred for treatment only for whom no followup was available were excluded from further analysis. The remaining 518 cases were followed until they were radiologically documented to be stone-free or considered treatment failures. Before ESWL additional procedures were performed in 144 patients, including stone push back, ureteral catheter or Double-J (Medical Engineering Corp., New York, New York) stent placement, percutaneous nephrostomy, ureteral endoscopic maneuvers or stone basket manipulation. A total of 374 patients needed no preliminary treatment before ESWL. RESULTS: Of the 518 patients 469 (91%) were successfully treated with 1 ESWL session, while 49 (9%) needed 2 or 3. Manipulation after ESWL was performed in 22 cases, including stent placement, percutaneous nephrostomy, ureteral endoscopic stone removal and a stone basket procedure. On day 1 after ESWL 327 patients (63%) were stone-free, 158 (30%) had less than 5 mm. fragments and 33 (7%) had more than 5 mm. fragments. At 3 months the stone-free rate increased to 97%. CONCLUSIONS: These data show that ESWL for distal ureteral calculi with the powerful unmodified HM3 lithotriptor has a high success rate with a low rate of minimally traumatic manipulations before and after intervention. Results in terms of the re-treatment and stone-free rates are superior to those of any other second or third generation lithotriptor and comparable to the results of the best ureteroscopic series.

Cardiac Shock Wave Therapy for Chronic Refractory Angina Pectoris. A Prospective Placebo-Controlled Randomized Trial

Background: Cardiac shock wave therapy (CSWT) delivered to the myocardium increases capillary density and regional myocardial blood flow in animal experiments. In addition, nonenzymatic nitric oxide production and the upregulation of vascular growth factor's mRNA by CSWT have been described. The aim of the study was therefore to test its potential to relieve symptoms in patients with chronic stable angina pectoris. Methods: Twenty-one patients (mean age 68.2 ± 8.3 years, 19 males) with chronic refractory angina pectoris and evidence of inducible myocardial ischemia during MIBI-SPECT imaging, were randomized into a treatment (n = 11) and a placebo arm (n = 10). The region of exercise-induced ischemia was treated with echocardiographic guidance during nine sessions over a period of 3 months. One session of CSWT consisted of 200 shots/spot (9--12 spots/session) with an energy intensity of 0.09 mJ/mm2. In the control group acoustic simulation was performed without energy application. Medication was kept unchanged during the whole treatment period. Results: In the treatment group, symptoms improved in 9/11 patients, and the ischemic threshold, determined by cardiopulmonary exercise stress testing, increased from 80 ± 28 to 95 ± 28 W (P= 0.036). In the placebo arm, only 2/10 patients reported an improvement and the ischemic threshold remained unchanged (98 ± 23 to 107 ± 23 W; P= 0.141). The items “physical functioning” (P= 0.043), “general health perception” (P= 0.046), and “vitality” (P= 0.035) of the SF-36 questionnaire significantly improved in the treatment arm, whereas in the placebo arm, no significant change was noted. Neither arrhythmias, troponin rise nor complications were observed during treatment. Conclusions: This placebo controlled trial shows a significant improvement in symptoms, quality of life parameters and ischemic threshold during exercise in patients with chronic refractory angina pectoris treated with CSWT. Thus, CSWT represents a new option for the treatment of patients with refractory AP.

Extracorporeal shock wave therapy as a treatment of a non-healing chronic leg ulcer

Extracorporeal shock waves are defined as a sequence of sonic pulses characterized by high peak pressure over 100 MPa, fast pressure rise, and short lifecycle. In the 1980s extracorporeal shock wave lithotripsy (ESWL) was first used for the treatment of urolithiasis. Orthopedic surgeons use extracorporeal shock wave therapy (ESWT) to treat non-union fractures, tendinopathies and osteonecrosis. The first application of ESWT in dermatology was for recalcitrant skin ulcers. Several studies in the last 10 years have shown that ESWT promotes angiogenesis, increases perfusion in ischemic tissues, decreases inflammation, enhances cell differentiation and accelerates wound healing. We successfully treated a non-healing chronic venous leg ulcer with ESWT. Furthermore we observed an improvement of the lymphatic drainage after application of ESWT. We are confident that ESWT is a non-invasive, practical, safe and efficient physical treatment modality for recalcitrant leg ulcers.

Optimization of extracorporeal shock wave lithotripsy delivery rates achieves excellent outcomes in ureteral stones. Results of a prospective, randomized trial

PURPOSE Management of ureteral stones remains controversial. To determine whether optimizing extracorporeal shock wave lithotripsy (ESWL) delivery rates improves treatment of solitary ureteral stones, we compared outcomes of two SW delivery rates in a prospective, randomized trial. MATERIALS AND METHODS From July 2010 to October 2012, 254 consecutive patients were randomized to undergo ESWL at SW delivery rates of either 60 pulses (n=130) or 90 pulses (n=124) per min. The primary endpoint was stone-free rate at 3-month follow-up. Secondary endpoints included stone disintegration, treatment time, complications, and the rate of secondary treatments. Descriptive statistics were used to compare endpoints between the two groups. Adjusted odds ratios and 95% confidence intervals were calculated to assess predictors of success. RESULTS The stone-free rate at 3 months was significantly higher in patients who underwent ESWL at a SW delivery rate of 90 pulses per min than in those receiving 60 pulses (91% vs. 80%, p=0.01). Patients with proximal and mid-ureter stones, but not those with distal ureter stones, accounted for the observed difference (100% vs. 83%; p=0.005; 96% vs. 73%, p=0.03; and 81% vs. 80%, p=0.9, respectively). Treatment time, complications, and the rate of secondary treatments were comparable between the two groups. In multivariable analysis, SW delivery rate of 90 pulses per min, proximal stone location, stone density, stone size and the absence of an indwelling JJ stent were independent predictors of success. CONCLUSIONS Optimization of ESWL delivery rates can achieve excellent results for ureteral stones.

Extracorporeal shock wave therapy for injection site panniculitis in multiple sclerosis patients.

BACKGROUND Painful cutaneous injection site reactions may hamper treatment with interferon β (IFN-β) and glatiramer acetate (GA) in multiple sclerosis (MS) patients. OBJECTIVE To maintain therapy adherence, efficient therapeutic modalities for these subcutaneous inflammatory lesions are urgently needed. We tested the application of local extracorporeal shock wave therapy (ESWT). METHODS We applied 5 sessions of ESWT to 8 patients suffering from MS who had developed painful panniculitis at the injection sites of either IFN-β or GA. Clinical outcomes, i.e. pain reduction and regression of induration, were assessed 3 and 6 months after completion of the ESWT using a visual analogue score. RESULTS All patients showed both significant pain reduction and reduction of the skin induration in the treated lesions, while in untreated control lesions there was no improvement. CONCLUSION ESWT proved to be a non-invasive, safe and efficient physical treatment modality for injection-induced painful cutaneous side effects of disease-modifying drugs in MS. © 2014 S. Karger AG, Basel.

Modified double-slit interferometer for shock-wave investigations.

"This work was carried out as part of Project SQUID which is supported by the Office of Naval Research under Contract Nonr-1858 (25)."

Normal shock wave parameters in equilibrium air,

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Investigation of small surface protuberances upstream of turbulent boundary layer separation produced by a skewed shock wave at Mach 3 /

"Interim report for period January 1976-February 1976."

Axisymmetric shock wave interaction with a cone: a benchmark test

Results of the benchmark test are presented of comparing numerical schemes solving shock wave of M-s = 2.38 in nitrogen and argon interacting with a 43 degrees semi-apex angle cone and corresponding experiments. The benchmark test was announced in Shock Waves Vol. 12, No. 4, in which we tried to clarify the effects of viscosity and heat conductivity on shock reflection in conical flows. This paper summarizes results of ten numerical and two experimental applications. State of the art in studies regarding the shock/cone interaction is clarified.