We consider self-similar measures µ with support in the interval 0 ≤ x ≤ 1 which have the analytic functions e i2πnx : n = 0, 1, 2, . . . span a dense subspace in L 2 (µ). Depending on the fractal dimension of µ, we identify subsets P ⊂ N 0 = {0, 1, 2, . . . } such that the functions {en : n ∈ P } form an orthonormal basis for L 2 (µ). We also give a higher-dimensional affine construction leading to self-similar measures µ with support in R ν . It is obtained from a given expansive ν-by-ν matrix and a finite set of translation vectors, and we show that the corresponding L 2 (µ) has an orthonormal basis of exponentials e i2πλ•x , indexed by vectors λ in R ν , provided certain geometric conditions (involving the Ruelle transfer operator) hold for the affine system.

This study presents the first histopathological validation of CMR and endocardial voltage mapping to define acute and chronic atrial ablation injury, including SI thresholds that best match histological lesion volumes. An understanding of these thresholds may allow a more informed assessment of the underlying atrial substrate immediately after ablation and before repeat catheter ablation for atrial arrhythmias.

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BackgroundIntramyocardialhemorrhage (IMH) reflects severe reperfusion injury in acute myocardial infarction. Non-invasive detection of IMH by cardiovascular magnetic resonance (CMR) may serve as a surrogate marker to evaluate the effect of preventive measures to reduce reperfusion injury and hence provide additional prognostic information. We sought to investigate whether IMH could be detected by CMR exploiting the T1 shortening effect of methemoglobin in an experimental model of acute myocardial infarction. The results were compared to T2-weighthed short tau inversion recovery (T2-STIR), and T2*-weighted(T2*W) sequences.Methods and resultsIMH was induced in ten 40 kg pigs by 50-min balloon occlusion of the mid LAD followed by reperfusion. Between 4–9 days (average 4.8) post-injury, the left ventricular myocardium was assessed by T1-weigthed Inversion Recovery(T1W-IR), T2-STIR, and T2*Wsequences. All CMR images were matched to histopathology and compared with the area of IMH. The difference between the size of the IMH area detected on T1W-IR images and pathology was −1.6 ± 11.3% (limits of agreement, -24%–21%), for the T2*W images the difference was −0.1 ± 18.3% (limitsof agreement, -36.8%–36.6%), and for T2-STIR the difference was 8.0 ± 15.5% (limits of agreement, -23%–39%). By T1W IR the diagnostic sensitivity of IMH was 90% and specificity 70%, for T2*W imaging the sensitivity was 70% and specificity 50%, and for T2-STIR sensitivity for imaging IMH was 50% and specificity 60%.ConclusionT1-weigthednon-contrast enhanced CMR detects IMH with high sensitivity and specificity and may become a diagnostic tool for detection of IMH in patients with myocardial infarction.

The efficacy of cardioprotective strategies can be quantified by myocardial salvage as an indicator of therapeutic benefit. Salvage is calculated as the difference between the area at risk (AAR) and the final infarct size (FIS). AAR has been quantified by angiographic assessment followed by quantification of FIS by biochemical ischaemic markers or imaging modalities such as cardiovascular magnetic resonance (CMR). Angiographical methods may overestimate AAR and since methodological differences may exist between different modalities, the use of different modalities for estimating AAR and FIS may not be recommended. (99m)Technetium (Tc)-Sestamibi single-photon emission tomography (SPECT) allows quantification of AAR and FIS by tracer injection prior to revascularization and after 1 month, respectively. SPECT provides the most validated measure of myocardial salvage and has been utilized in multiple randomized clinical trials. However, SPECT is logistically challenging, expensive, and includes radiation exposure. More recently, a large number of studies have suggested that CMR can determine salvage in a single examination by combining measures of myocardial oedema in the AAR exposed to ischaemia reperfusion with FIS quantification by late gadolinium enhancement. The T1- and T2-weighted CMR approaches for quantification of AAR utilize non-contrast, early and late gadolinium enhancement techniques. The technical progress, high spatial resolution and the potential for retrospective quantification of the AAR makes CMR the most appropriate technique for assessment of myocardial salvage. However, the optimum CMR technique for assessment of myocardial AAR remains to be defined. Consequently, we recommend a comprehensive CMR protocol to ensure reliable assessment of myocardial salvage.

Several studies indicate that a biochemically reduced response to aspirin increases the risk of cardiovascular events. This study was designed to investigate the performance of Multiplate whole blood aggregometry as regards assessment of platelet function prior to and after aspirin treatment, and to compare it with light transmission aggregometry (LTA). We included 21 healthy individuals and 43 patients with documented coronary artery disease (CAD). Platelet aggregation induced by arachidonic acid 0.5 mM was measured in duplicate by Multiplate aggregometry and LTA in healthy individuals before aspirin treatment and in all participants on four consecutive days during treatment with 75 mg aspirin daily. Optimal compliance was confirmed by complete suppression of serum thromboxane B(2) in all participants. Employing the Multiplate, the coefficient of variation (CV) was lower at baseline (CV = 8%) than during aspirin treatment in both healthy individuals (CV = 46%) and patients (CV = 46%). During aspirin treatment, the repeatability of LTA was superior to Multiplate measurements. However, the Multiplate was superior to LTA as regards the ability to discriminate platelet response before and after aspirin treatment. In conclusion, the repeatability of Multiplate aggregometry was good before aspirin treatment, whereas the CV was quite high during aspirin treatment in both healthy individuals and patients. However, the Multiplate device was fully capable of assessing platelet function prior to and after treatment with aspirin. Clinical studies are needed to investigate whether a high platelet aggregation level measured by Multiplate whole blood aggregometry during aspirin treatment is associated with a poor clinical outcome.

Abstract. We consider affine systems in R n constructed from a given integral invertible and expansive matrix R, and a finite set B of translates, σ b x := R −1 x + b; the corresponding measure µ on R n is a probability measure and fixed by the selfsim-b . There are two a priori candidates for an associated orthogonal harmonic analysis : (i) the existence of some subset Λ in R n such that the exponentials {e iλ·x } λ∈Λ form an orthogonal basis for L 2 (µ); and (ii) the existence of a certain dual pair of representations of the C * -algebra O N where N is the cardinality of the set B. (For each N , the C * -algebra O N is known to be simple; it is also called the Cuntz-algebra.) We show that, in the "typical" fractal case, the naive version (i) must be rejected; typically the orthogonal exponentials in L 2 (µ) fail to span a dense subspace. Instead we show that the C * -algebraic version of an orthogonal harmonic analysis, viz., (ii), is a natural substitute. It turns out that this version is still based on exponentials e iλ·x , but in a more indirect way. (See details in Section 5 below.) Our main result concerns the intrinsic geometric features of affine systems, based on R and B, such that µ has the C * -algebra property (ii). Specifically, we show that µ has an orthogonal harmonic analysis (in the sense (ii)) if the system (R, B) satisfies some specific symmetry conditions (which are geometric in nature). Our conditions for (ii) are stated in terms of two pieces of data: (a) a unitary generalized Hadamard-matrix , and (b) a certain system of lattices which must exist and, at the same time, be compatible with the Hadamard-matrix. A partial converse to this result is also given. Several examples are calculated, and a new maximality condition for exponentials is identified.