Scaling laws of failure dynamics on complex networks.

The topology of the network of load transmitting connections plays an essential role in the cascading failure dynamics of complex systems driven by the redistribution of load after local breakdown events. In particular, as the network structure is gradually tuned from regular to completely random a transition occurs from the localized to mean field behavior of failure spreading. Based on finite size scaling in the fiber bundle model of failure phenomena, here we demonstrate that outside the localized regime, the load bearing capacity and damage tolerance on the macro-scale, and the statistics of clusters of failed nodes on the micro-scale obey scaling laws with exponents which depend on the topology of the load transmission network and on the degree of disorder of the strength of nodes. Most notably, we show that the spatial structure of damage governs the emergence of the localized to mean field transition: as the network gets gradually randomized failed clusters formed on locally regular patches merge through long range links generating a percolation like transition which reduces the load concentration on the network. The results may help to design network structures with an improved robustness against cascading failure.

Gastrointestinal Angiodysplasia in Patients with Severe Aortic Stenosis: The Endoscopic Features of Heyde's Syndrome.

INTRODUCTION: Aortic stenosis (AS) is sometimes associated with gastrointestinal bleeding, and this phenomenon is known as Heyde's syndrome. Such bleeding is most often considered to originate from gastrointestinal angiodysplasias, but the frequency and endoscopic features of such bleeding remain unclear. This study aimed to determine the frequency and endoscopic features of gastrointestinal angiodysplasia in patients with severe AS. PATIENTS AND METHODS: In this multicenter, retrospective study, we evaluated consecutive patients who underwent transcatheter aortic valve implantation (TAVI) with severe AS from May 2016 to December 2019. We extracted the data on the clinicopathological features according to the status of anemia, the proportion of patients who underwent gastrointestinal endoscopic examinations and demonstrated gastrointestinal angiodysplasia, and identified the endoscopic features associated with such patients. RESULTS: In 325 patients, the rates of moderate/severe anemia (hemoglobin < 11 g/dL) were 52%. Regarding medicine, there were no significant differences between the patients with and without moderate/severe anemia. Patients were examined by esophagogastroduodenoscopy (21%), colonoscopy (12%), and balloon-assisted enteroscopy or small bowel capsule endoscopy (1.5%). Patients with moderate/severe anemia had significantly more angiodysplasia (38.3% vs. 7.7%; p < 0.0001) and active bleeding (23.4% vs. 0%; p < 0.01). Angiodysplasia was detected in 21 patients (stomach, n = 9; small intestine, n = 5, and colon, n = 10). CONCLUSIONS: The results suggest, for the first time, that patients with severe AS who underwent TAVI and moderate/severe anemia frequently had gastrointestinal angiodysplasia and active bleeding throughout the entire gastrointestinal tract.

Doppler Underestimates Transvalvular Gradient Measured by Catheterization in Patients With Severe Aortic Stenosis.

We sought to clarify characteristics of patients with severe aortic stenosis (AS) in whom transvalvular mean pressure gradient (MPG) was underestimated with Doppler compared with catheterization. Study subjects included 127 patients with severe AS who underwent transcatheter aortic valve implantation. Between subjects with Doppler MPG underestimation ≥10 mm Hg (group U) and those without (group C), we retrospectively compared echocardiographic parameters and aortic valve calcification score using the Agatston method. Despite a strong correlation (rS = 0.88) and small absolute difference (2.1 ± 10.1 mm Hg) between Doppler and catheter MPG, 27 patients (21%) were in group U. Among 48 patients with catheter MPG ≥60 mm Hg, 10 patients (21%) revealed Doppler MPG of 40 to 59 mm Hg, suggesting they had been misclassified as having severe AS instead of very severe AS. According to the guidelines, indication of valve replacement for patients without symptoms should be considered for very severe AS but not for severe AS. Therefore, sole reliance on Doppler MPG could cause clinical misjudgments. Group U had larger relative wall thickness (median [interquartile range: 0.60 [0.50 to 0.69] vs 0.53 [0.46 to 0.60], p = 0.003) and higher calcification score (3,024 [2,066 to 3,555] vs 1,790 [1,293 to 2,501] arbitrary units, p <0.001). Both calcification score (per 100 arbitrary unit increment, odds ratio 1.10, 1.04 to 1.17, p = 0.002) and relative wall thickness (per 0.05 increment, odds ratio 1.29, 95% confidence interval 1.05 to 1.60, p = 0.02) were independently associated with Doppler underestimation. In conclusion, Doppler might underestimate transvalvular gradient compared with catheterization in patients with severe AS who have heavy valve calcification and prominent concentric remodeling left ventricular geometry.

Left ventricular hypertrophy as a predictor of cardiovascular outcomes after transcatheter aortic valve replacement.

AIMS: This study aimed to clarify the relationship between cardiovascular prognosis and left ventricular hypertrophy (LVH) in patients with severe aortic stenosis who underwent transcatheter aortic valve replacement (TAVR) and to investigate the relationship between cardiac sympathetic nerve (CSN) function and these factors using 123 I-metaiodobenzylguanidine scintigraphy. METHODS AND RESULTS: In this single-centre, retrospective observational study, 349 patients who underwent TAVR at our institution between July 2017 and May 2020 were divided into two groups: those with severe LVH pre-operatively [severe LVH (+) group] and those without LVH pre-operatively [severe LVH (-) group]. The rates of freedom from cardiovascular events (cardiovascular death and heart failure hospitalization) were compared. The relationship between changes in left ventricular mass index (LVMi) and changes in delay heart-mediastinum ratio (H/M) from before TAVR to 6 months after TAVR was also investigated. The event-free rate was significantly lower in the severe LVH (+) group (87.1% vs. 96.0%, log-rank P = 0.021). The severe LVH (+) group exhibited a significantly lower delay H/M value, scored by 123 I-metaiodobenzylguanidine scintigraphy, than the severe LVH (-) group (2.33 [1.92-2.67] vs. 2.67 [2.17-3.68], respectively, P < 0.001). Moreover, the event-free rate of post-operative cardiovascular events was lower among patients with a delay H/M value < 2.50 than that among other patients (87.7% vs. 97.2%, log-rank P = 0.012). LVMi was significantly higher (115 [99-130] vs. 90 [78-111] g/m2 , P < 0.001) and delay H/M value was significantly lower (2.53 [1.98-2.83] vs. 2.71 [2.25-3.19], P = 0.025) in the severe LVH (+) group than in the severe LVH (-) group at 6 months after TAVR. Patients with improved LVH at 6 months after TAVR also had increased delay H/M (from 2.51 [2.01-2.81] to 2.67 [2.26-3.02], P < 0.001), whereas those without improved LVH had no significant change in delay H/M (from 2.64 [2.23-3.06] to 2.53 [1.97-3.00], P = 0.829). CONCLUSIONS: Severe LVH before TAVR is a prognostic factor for poor post-operative cardiovascular outcomes. LVH associated with aortic stenosis and CSN function are correlated, suggesting their involvement in LVH prognosis.

Hotspot analysis of COVID-19 infection using mobile-phone location data.

Restrictions on outdoor activities are required to suppress the COVID-19 pandemic. To monitor social risks and control the pandemic through sustainable restrictions, we focus on the relationship between the number of people going out and the effective reproduction number. The novelty of this study is that we have considered influx population instead of staying-population, as the data represent congestion. This enables us to apply our analysis method to all meshes because the influx population may always represent the congestion of specific areas, which include the residential areas as well. In this study, we report the correlation between the influx population in downtown areas and business districts in Tokyo during the pandemic considering the effective reproduction number and associated time delay. Moreover, we validate our method and the influx population data by confirming the consistency of the results with those of the previous research and epidemiological studies. As a result, it is confirmed that the social risk with regard to the spread of COVID-19 infection when people travel to downtown areas and business districts is high, and the risk when people visit only residential areas is low.

Cystatin C in risk prediction after transcatheter aortic valve replacement: a retrospective analysis.

AIMS: No study has evaluated the prognostic value of the chronic kidney disease (CKD) classification by cystatin C-based estimated glomerular filtration rate (eGFR) (CKDCys classification) in patients undergoing transcatheter aortic valve replacement (TAVR). This study aimed to compare the prognostic value of CKDCys classification and CKD classification by creatinine-based eGFR (CKDCr classification) in risk prediction after TAVR. METHODS AND RESULTS: We retrospectively analysed consecutive 219 patients with symptomatic severe aortic stenosis who underwent TAVR at our institute between December 2016 and June 2019. Pre-operative CKDCr and CKDCys classifications were evaluated for their prognostic value of 2-year major adverse cardiovascular and cerebrovascular events (MACCE) after TAVR. MACCE was defined as the composite of all-cause mortality, non-fatal myocardial infarction, stroke, and rehospitalization for worsening congestive heart failure. Participants had a median age of 86.0 years and were predominantly female (76.9%). In 96.6% of the cases, TAVR was performed using transfemoral access. The median creatinine-based eGFR (52.85 mL/min/1.73 m2 ) was higher than the cystatin C-based eGFR (41.50 mL/min/1.73 m2 ). Downward reclassification in CKD stages based on eGFRCys was observed in 49.0% of patients. During a median follow-up period of 575.5 (interquartile range: 367.0-730.0) days, 58 patients presented with MACCE. CKDCys classification, but not CKDCr classification, significantly stratified the risk of 2-year MACCE in patients after TAVR by log-rank test (P = 0.003). In multivariate Cox regression analysis, only CKDCys stage 3b [hazard ratio (HR) = 4.37; 95% confidence interval (CI): 1.28-14.91; P = 0.019] and CKDCys stage 4 + 5 (HR = 3.72; 95% CI: 1.06-12.99; P = 0.040) were significant predictors of MACCE after adjustment for potential confounders. CONCLUSIONS: The CKDCys classification could better assess the risk than the CKDCr classification in patients undergoing TAVR. CKDCys stage 3b and stage 4 + 5 correlated with adverse outcomes.

Incidence and predictors of transcatheter aortic valve replacement device emboligenic matter detected by transesophageal echocardiography.

During transfemoral (TF) or transcatheter aortic valve replacement (TAVR), transesophageal echocardiography (TEE) sometimes reveals an unexpected mobile membranous mass on the catheter tip within the proximal part of the descending thoracic aorta. Such mobile masses may cause critical embolic events if the TAVR device advances into the ascending aorta in the absence of preventive measures. This study aimed to investigate the incidence and predictors of emboligenic matter (EM) during TAVR, impact of EM on the procedure, and incidence of symptomatic ischemic stroke post procedure. Among 436 consecutive patients who underwent TF-TAVR, 407 were evaluated in this study. The primary end point was incidence of symptomatic ischemic stroke within 24 h post procedure while taking appropriate preventive measures. Incidence of EM, factors associated with EM, and the impact of EM on the procedure were also investigated. Among the 407 cases, 15 cases (3.7%) of EM were identified but no ischemic stroke occurred in the EM (+) group (0% vs. 2.04%, p = 1.00). In the EM (+) group, a self-expandable valve was used in all 15 cases (100% vs. 42.6%, p < 0.0001) while 14 cases used a CoreValve's InLine sheath system initially (93.3% vs. 27.3%, p < 0.0001). CoreValve's InLine sheath system usage was the only independent predictor of EM. The CoreValve's InLine delivery system was identified as a predictor of EM during TF-TAVR, but symptomatic ischemic stroke was avoided while taking appropriate embolization preventive measures.

Serial changes in cardiac sympathetic nervous function after transcatheter aortic valve replacement: A prospective observational study using 123I-meta-iodobenzylguanidine imaging.

BACKGROUND: Transcatheter aortic valve replacement (TAVR) can rapidly improve cardiac sympathetic nervous function (CSNF) within 2 weeks in patients with aortic stenosis (AS). However, whether such short-term improvements will be sustained thereafter remains unclear. METHODS: Patients with severe AS who underwent TAVR between October 2017 and June 2019 were enrolled in this single-center, prospective, observational study. 123I-meta-iodobenzylguanidine imaging was performed at baseline, within 2 weeks after TAVR, and at 6 to 12 months post-TAVR to evaluate the heart-mediastinum ratio (H/M) and washout rate. RESULTS: Of 183 consecutive patients, 75 (19 men; median age: 86 years) were evaluated. The late H/M significantly improved within 2 weeks after TAVR (P = .041) and further improved over 6 to 12 months after TAVR (P = .041). Multivariate analysis revealed that the baseline mean aortic valve pressure gradient (mPG) was an independent predictor of mid-term improvement in the late H/M (> 0.1) (P = .037). Patients with a high baseline mPG (≥ 58 mmHg) exhibited a significantly greater increase in the late H/M than those with a low baseline mPG (< 42 mmHg) (0.24 vs 0.01; P = .029). CONCLUSION: CSNF demonstrated sustained improvement from within 2 weeks after TAVR until 6 to 12 months later. Such improvement was related to baseline hemodynamic AS severity.

Recapture failure in transcatheter aortic valve replacement with CoreValve Evolut R.

Self-expanding prostheses for transcatheter aortic valve replacement (TAVR), which can be recaptured, provide us the option of repositioning for a more accurate placement. We report a very rare case in which the recapture of CoreValve Evolut R (Medtronic, Minneapolis, Minnesota) to correct the implantation depth during the deployment could not be achieved. We planned TAVR with a 23 mm Evolut R prosthesis for a 92-year-old female with severe aortic stenosis and tightly bent thoracic aorta. During the first deployment attempt, the implantation depth was greater than we expected at 2/3 deployment. They tried to recapture and reposition the prosthesis, but the prosthesis was not re-sheathed into the capsule of the delivery system. The prosthesis could not be recaptured despite a repeat attempt, and they were forced to deploy the device as it was. The prosthesis was deployed very carefully and implanted successfully without a pop-up into the ascending aorta. At a later date, this situation was replicated in vitro and was found that the distal segment of the capsule became deformed, increasing the resistance to rotating the grip handle.

Prognostic value of cardiac 123 I-metaiodobenzylguanidine imaging for predicting cardiac events after transcatheter aortic valve replacement.

AIMS: In patients with aortic valve stenosis (AS), cardiac sympathetic nervous (CSN) dysfunction and its improvement after transcatheter aortic valve replacement (TAVR) have been reported. The prognostic impact of CSN function remains unclear. This study investigated the prognostic value of cardiac 123 I-metaiodobenzylguanidine (MIBG) imaging for predicting cardiac events after TAVR. METHODS AND RESULTS: This single-centre prospective observational study enrolled patients with AS between July 2017 and May 2019. MIBG scintigraphy was performed before and soon after TAVR to evaluate the late heart-mediastinum ratio (L-H/M). Patients were classified into three pairs of groups based on the baseline and post-TAVR L-H/M (≥2.0 or <2.0) and on the presence of TAVR-related improvement in L-H/M. The study endpoint was the occurrence of major adverse cardiac events (MACE), defined as a composite of all-cause death, non-fatal myocardial infarction, and hospitalization due to heart failure. Among the 187 consecutive patients who underwent TAVR, 107 (27 men; median age: 86 years) were evaluated. Over a median follow-up of 366 days, 15 (14.0%) patients had MACE. The incidence of MACE was significantly low in patients with L-H/M improvement and/or high post-TAVR L-H/M (≥2.0). Baseline L-H/M and frailty were associated with poor response of L-H/M to TAVR treatment. TAVR-related improvement in L-H/M had significant effects on MACE, with an adjusted hazard ratio of 0.233 (95% confidence interval, 0.064-0.856; P = 0.028). CONCLUSIONS: TAVR-related improvement in L-H/M was an independent predictor of cardiac events, 1 year after TAVR. Cardiac MIBG imaging is useful for predicting cardiac events after TAVR.

Comparative Analysis of the Paclitaxel-Eluting Peripheral Igaki-Tamai Stent and the Drug-Free Igaki-Tamai Stent Using Optical Coherence Tomography and Histological Analysis in a Porcine Iliac Artery Model.

BACKGROUND: The combination of a bioresorbable scaffold and antiproliferative drugs is a promising treatment for peripheral artery disease. The novel paclitaxel-eluting peripheral Igaki-Tamai stent (PTX-ITS) has the same backbone design as the drug-free peripheral Igaki-Tamai stent and a paclitaxel coating. Arterial responses to the PTX-ITS and ITS using optical coherence tomography (OCT) and histological analysis in a porcine iliac artery model were compared.Methods and Results:In total, 6 PTX-ITSs and 6 ITSs implanted in porcine iliac arteries were evaluated. Quantitative measurements of the scaffold, lumen, neointimal areas, and percent area stenosis were performed using OCT at 1 and 3 months. Histological evaluations (PTX-ITS [n=5], ITS [n=4]) were performed following euthanasia at 3 months. Injury, inflammation, endothelialization, and fibrin scores were measured. Baseline angiographic characteristics were similar in both groups. The ITS group showed significantly smaller scaffold areas than the PTX-ITS group at 1 month (18.50±3.62 mm2vs. 23.54±3.64 mm2; P=0.037) and 3 months (15.82±2.57 mm2vs. 21.67±3.57 mm2; P=0.009). Percent area stenosis was significantly lower in the PTX-ITS group at 3 months (28.70±7.24% vs. 40.36±7.07%; P=0.018). Histological evaluations revealed similar low-grade inflammatory reactions for both scaffolds. CONCLUSIONS: PTX-ITSs showed significantly better suppression of late scaffold shrinkage and lower in-scaffold stenosis for up to 3 months. Additionally, PTX-ITSs exhibited high biocompatibility, which is comparable to ITSs.

Importance of Preoperative Computed Tomography Assessment of the Membranous Septal Anatomy in Patients Undergoing Transcatheter Aortic Valve Replacement With a Balloon-Expandable Valve.

BACKGROUND: Cardiac conduction disturbance (CD) is the most frequent complication following transcatheter aortic valve replacement (TAVR). This study examined whether the anatomy of the membranous septum (MS) could provide useful information about the risk of CD following TAVR with a balloon-expandable valve (BEV).Methods and Results:Among 132 consecutive patients, 106 (mean age, 85.6±5.1 years; 75 females) were included in the study. Using preoperative CT and angiography, MS length and implantation depth (ID) were assessed. The MS length minus the prosthesis ID was calculated (∆MSID). Correlation between CD, defined as new-onset left-bundle branch block (LBBB) or the need for permanent pacemaker (PPM) within 1 week after the procedure, and MS length were evaluated. A total of 19 patients (18%) developed CD following TAVR. MS length was significantly shorter in these patients than in those without CD (5.3±1.3 vs. 6.6±1.4; P<0.001), and was the important predictor of CD (odds ratio [OR]: 0.43, 95% confidence interval [CI]: 0.27-0.69, P<0.001). When considering the pre- and postprocedural parameters, the ∆MSID was smaller in patients with CD (-1.7±1.5 vs. 0.8±1.9, P<0.001), and emerged as the important predictor of CD (OR: 0.47, 95% CI: 0.33-0.69, P<0.001). CONCLUSIONS: Short MS is associated with an increased risk of CD after TAVR with BEV.

Early effects of transcatheter aortic valve replacement on cardiac sympathetic nervous function assessed by 123I-metaiodobenzylguanidine scintigraphy in patients with severe aortic valve stenosis.

PURPOSE: The effects of transcatheter aortic valve replacement (TAVR) on cardiac sympathetic nervous (CSN) function have not been fully explored. This study aimed to investigate the early (within 2 weeks) effects of TAVR on CSN function in patients with severe aortic valve stenosis (AS) using 123I-metaiodobenzylguanidine (MIBG) scintigraphy. METHODS: Of 143 consecutive patients who were scheduled to undergo TAVR, 67 (18 men; median age 86 years) were evaluated in this single-centre prospective observational study. MIBG scintigraphy was performed at baseline and 3-14 days after the TAVR procedure to evaluate the heart-mediastinum ratio (H/M) and washout rate (WR). Differences between baseline and post-TAVR MIBG parameters were analysed. MIBG parameter changes were compared with echocardiographic parameters. Furthermore, factors involved in the improvement in MIBG parameters were investigated. RESULTS: All patients successfully underwent TAVR with improved echocardiographic parameters, including aortic valve area (AVA; 0.6 cm2 vs. 1.6 cm2), peak velocity (4.5 m/s vs. 2.0 m/s), mean pressure gradient (50 mmHg vs. 9 mmHg), and left ventricular ejection fraction (56% vs. 62%) (all p < 0.001). On MIBG imaging, delayed H/M significantly increased (2.57 vs. 2.68, p < 0.001), whereas WR decreased (32.2% vs. 26.8%, p < 0.001). In multivariate analysis, higher baseline WR was associated with improvement in WR (> 3%). Female sex, Clinical Frailty Scale score ≤ 5, baseline estimated glomerular filtration rate, and baseline AVA were predictors of improvement in delayed H/M (> 0.1). Baseline AVA and E/E' were independent predictors of improvement in both WR and delayed H/M. CONCLUSIONS: The CSN function was impaired in patients with AS, as assessed using MIBG scintigraphy. WR and delayed H/M improved immediately after TAVR. Improvement in CSN function may be related to echocardiographic AS severity at baseline before TAVR.

Transcatheter Aortic Valve Implantation for Degenerated 19-mm Aortic Bioprosthetic Valve.

BACKGROUND: The valve-in-valve procedure, in which a transcatheter heart valve (THV) is implanted over a prosthetic valve, has been shown to be safe and therapeutically effective, depending on the size of the replacement valve.Methods and Results:We report 3 cases of successful valve-in-valve procedure to replace a degenerated 19-mm stented prosthetic aortic valve. Balloon-expanding THVs were implanted: 20-mm in the 1st case and 23-mm in the next 2. Aortic stenosis was almost completely resolved in all patients, who recovered promptly and without cardiac adverse events. CONCLUSIONS: Using the valve-in-valve procedure for a 19-mm degenerated bioprosthesis was feasible and safe.

Splash detail due to a single grain incident on a granular bed.

Using the discrete element method, we study the splash processes induced by the impact of a grain on a randomly packed bed. Good correspondence is obtained between our numerical results and the findings of previous experiments for the movement of ejected grains. Furthermore, the distributions of the ejection angle and ejection speed for individual grains vary depending on the relative timing at which the grains are ejected after the initial impact. Obvious differences are observed between the distributions of grains ejected during the earlier and later splash periods: the form of the vertical ejection-speed distribution varies from a power-law form to a lognormal form with time; this difference may determine grain trajectory after ejection.

Ripening kinetics of bubbles: A molecular dynamics study.

The ripening kinetics of bubbles is studied by performing molecular dynamics simulations. From the time evolution of a system, the growth rates of individual bubbles are determined. At low temperatures, the system exhibits a t1/2 law and the growth rate is well described by classical Lifshitz-Slyozov-Wagner (LSW) theory for the reaction-limited case. This is direct evidence that the bubble coarsening at low temperatures is reaction-limited. At high temperatures, although the system exhibits a t1/3 law, which suggests that it is diffusion-limited, the accuracy of the growth rate is insufficient to determine whether the form is consistent with the prediction of LSW theory for the diffusion-limited case. The gas volume fraction dependence of the coarsening behavior is also studied. Although the behavior of the system at low temperatures has little sensitivity to the gas volume fraction up to 10%, at high temperatures it deviates from the prediction of LSW theory for the diffusion-limited case as the gas volume fraction increases. These results show that the mean-field-like treatment is valid for a reaction-limited system even with a finite volume fraction, while it becomes inappropriate for a diffusion-limited system since classical LSW theory for the diffusion-limited case is valid at the dilute limit.

Order-disorder transition in repulsive self-propelled particle systems.

We study the collective dynamics of repulsive self-propelled particles. The particles are governed by coupled equations of motion that include polar self-propulsion, damping of velocity and of polarity, repulsive particle-particle interaction, and deterministic dynamics. Particle dynamics simulations show that the collective coherent motion with large density fluctuations spontaneously emerges from a disordered, isotropic state. In the parameter region where the rotational damping of polarity is strong, the system undergoes an abrupt shift to the absorbing ordered state after a waiting period in the metastable disordered state. In order to obtain a simple understanding of the mechanism underlying the collective behavior, we analyze the binary particle scattering process. We show that this approach correctly predicts the order-disorder transition at a dilute limit. The same approach is expanded for finite densities, although it disagrees with the result from many-particle simulations due to many-body correlations and density fluctuations.

Kinetic Monte Carlo algorithm for thermally induced breakdown of fiber bundles.

Fiber bundle models are one of the most fundamental modeling approaches for the investigation of the fracture of heterogeneous materials being able to capture a broad spectrum of damage mechanisms, loading conditions, and types of load sharing. In the framework of the fiber bundle model we introduce a kinetic Monte Carlo algorithm to investigate the thermally induced creep rupture of materials occurring under a constant external load. We demonstrate that the method overcomes several limitations of previous techniques and provides an efficient numerical framework at any load and temperature values. We show for both equal and localized load sharing that the computational time does not depend on the temperature; it is solely determined by the external load and the system size. In the limit of low load where the lifetime of the system diverges, the computational time saturates to a constant value. The method takes into account the secondary failures induced by subsequent load redistributions after breaking events, with the additional advantage that breaking avalanches always start from a single broken fiber.