Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces

In this article we present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model many different phenomena in areas such as developmental and cancer biology, cell motility and material science. Often one is interested in identifying parameters which will lead to a particular pattern. To attempt to answer this, we compute eigenpairs of the Laplacian on a variety of domains and use linear stability analysis to determine parameter values for the system that will lead to spatially inhomogeneous steady states whose patterns correspond to particular eigenfunctions. This method has previously been used on domains and surfaces where the eigenvalues and eigenfunctions are found analytically in closed form. Our contribution to this methodology is that we numerically compute eigenpairs on arbitrary domains and surfaces. Here we present various examples and demonstrate that mode isolation is straightforward especially for low eigenvalues. Additionally we see that if two or more eigenvalues are in a permissible range then the inhomogeneous steady state can be a linear combination of the respective eigenfunctions. Finally we show an example which suggests that pattern formation is robust on similar surfaces in cases that the surface either has or does not have a boundary.

Analysis of coronary bifurcations by intravascular ultrasound and virtual histology

Background Regional differences in shear stress have been identified as reason for early plaque formation in vessel bifurcations. We aimed to investigate regional plaque morphology and composition using intravascular ultrasound (IVUS) and virtual histology (IVUS–VH) in coronary artery bifurcations. Methods We performed IVUS and IVUS–VH studies at coronary bifurcations to analyze segmental plaque burden and composition of different segments in relation to their orientation to the bifurcation. Results A total of 236 patients with a mean age of 59 ± 11 years (69% male) were analyzed. Plaque burden was higher at the contralateral vessel wall facing the bifurcation compared to the ipsilateral vessel wall and this difference was true for proximal and distal segments (proximal: 37 ± 12% and 45 ± 15% for segments at the ipsilateral and contralateral vessel wall, respectively, p < 0.001; distal: 37 ± 10% and 47 ± 15% for segments at the ipsilateral and contralateral vessel wall, respectively, p < 0.001). In addition, these segments exhibited a higher proportion of dense calcium and a lower proportion of fibrous tissue and fibro fatty tissue. Conclusions Segments on the contralateral wall of the bifurcation which have previously been identified as regions with low shear stress not only exhibited a higher plaque burden, but also a higher degree of calcification.

Clinical outcomes after zotarolimus and everolimus drug eluting stent implantation in coronary artery bifurcation lesions: insights from the RESOLUTE All Comers Trial

OBJECTIVE We investigated clinical outcomes after treatment of coronary bifurcation lesions with second generation drug eluting stents (DES). DESIGN Post hoc analysis of a randomised, multicentre, non-inferiority trial. SETTING Multicentre study. PATIENTS All comers study with minimal exclusion criteria. INTERVENTIONS Patients were treated with either zotarolimus or everolimus eluting stents. The patient population was divided according to treatment of bifurcation or non-bifurcation lesions and clinical outcomes were compared between groups. MAIN OUTCOMES MEASURES Clinical outcomes within 2-year follow-up. RESULTS A total of 2265 patients were included in the present analysis. Two-year follow-up data were available in 2223 patients: 1838 patients in the non-bifurcation group and 385 patients in the bifurcation group. At 2-year follow-up the bifurcation and the non-bifurcation lesion groups showed no significant differences in terms of cardiac death (2.3 vs 2.1, p=0.273), target lesion failure (9.7% vs 13.8%, p=0.255), major adverse cardiac events (11.5% vs 15.1%, p=0.305), target lesion revascularisation (4.7% vs 6.0%, p=0.569), and definite or probable stent thrombosis (1.6% vs 1.8%, p=0.419). CONCLUSIONS The use of second generation DES for the treatment of coronary bifurcation lesions was associated with similar long term mortality and clinical outcomes compared with non-bifurcation lesions.

Three-year outcomes of percutaneous coronary intervention with next-generation zotarolimus-eluting stents for de novo coronary bifurcation lesions.

AIMS To investigate the outcomes of percutaneous coronary intervention (PCI) in bifurcation versus non-bifurcation lesions using the next-generation Resolute zotarolimus-eluting stent (R-ZES). METHODS AND RESULTS We analyzed 3-year pooled data from the RESOLUTE All-Comers trial and the RESOLUTE International registry. The R-ZES was used in 2772 non-bifurcation lesion patients and 703 bifurcation lesion patients, of which 482 were treated with a simple-stent technique (1 stent used to treat the bifurcation lesion) and 221 with a complex bifurcation technique (2 or more stents used). The primary endpoint was 3-year target lesion failure (TLF, defined as the composite of death from cardiac causes, target vessel myocardial infarction, or clinically-indicated target lesion revascularization [TLR]), and was 13.3% in bifurcation vs 11.3% in non-bifurcation lesion patients (adjusted P=.06). Landmark analysis revealed that this difference was driven by differences in the first 30 days between bifurcation vs non-bifurcation lesions (TLF, 6.6% vs 2.7%, respectively; adjusted P<.001), which included significant differences in each component of TLF and in-stent thrombosis. Between 31 days and 3 years, TLF, its components, and stent thrombosis did not differ significantly between bifurcation lesions and non-bifurcation lesions (TLF, 7.7% vs 9.0%, respectively; adjusted P=.50). CONCLUSION The 3-year risk of TLF following PCI with R-ZES in bifurcation lesions was not significantly different from non-bifurcation lesions. However, there was an increased risk associated with bifurcation lesions during the first 30 days; beyond 30 days, bifurcation lesions and non-bifurcation lesions yielded similar 3-year outcomes.

Anatomic characteristics and clinical implications of angiographic coronary thrombus: insights from a patient-level pooled analysis of SYNTAX, RESOLUTE, and LEADERS Trials.

BACKGROUND The distribution of thrombus-containing lesions (TCLs) in an all-comer population admitted with a heterogeneous clinical presentation (stable, ustable angina, or an acute coronary syndrome) and treated with percutaneous coronary intervention is yet unclear, and the long-term prognostic implications are still disputed. This study sought to assess the distribution and prognostic implications of coronary thrombus, detected by coronary angiography, in a population recruited in all-comer percutaneous coronary intervention trials. METHODS AND RESULTS Patient-level data from 3 contemporary coronary stent trials were pooled by an independent academic research organization (Cardialysis, Rotterdam, the Netherlands). Clinical outcomes in terms of major adverse cardiac events (major adverse cardiac events, a composite of death, myocardial infarction, and repeat revascularization), death, myocardial infarction, and repeated revascularization were compared between patients with and without angiographic TCL. Preprocedural TCL was present in 257 patients (5.8%) and absent in 4193 (94.2%) patients. At 3-year follow-up, there was no difference for major adverse cardiac events (25.3 versus 25.4%; P=0.683); all-cause death (7.4 versus 6.8%; P=0.683); myocardial infarction (5.8 versus 6.0%; P=0.962), and any revascularizations (17.5 versus 17.7%; P=0.822) between patients with and without TCL. The comparison of outcomes in groups weighing the jeopardized myocardial by TCL also did not show a significant difference. TCL were seen more often in the first 2 segments of the right (43.6%) and left anterior descending (36.8%) coronary arteries. The association of TCL and bifurcation lesions was present in 40.1% of the prespecified segments. CONCLUSIONS TCL involved mainly the proximal coronary segments and did not have any effect on clinical outcomes. A more detailed thrombus burden quantification is required to investigate its prognostic implications. CLINICAL TRIAL REGISTRATION URL: http://www.clinicaltrials.gov. Unique identifiers: NCT00114972, NCT01443104, NCT00617084.