INTEGRAL SOLUTIONS

We obtain the non-trival integral solutions for quartic Diaphoptine equations with two variables is presented. A few numerical examples are given

A case report of refractory angina in a patient with diabetes and apical hypertrophic cardiomyopathy

Background: Using serial imaging over time, this case reviews the natural history of co-morbid Type two diabetes (T2D) and apical hypertrophic cardiomyopathy (HCM) and assesses the potential combined impact on myocardial structure and perfusion. Case summary: A 59-year-old patient with concomitant T2D and an apical phenotype of HCM was seen over a 11-year period with a significant burden of anginal chest pain. Chest pain was refractory to anti-anginal medical therapy and persisted at on-going follow-up. Multi-modality imaging demonstrated significant deterioration in coronary microvascular function and increased myocardial scar burden despite unobstructed epicardial coronary arteries. Discussion: Comorbidity with T2D and apical HCM resulted in a significant increase in myocardial fibrosis and deterioration in coronary microvascular function

Multiple Etiologies to Myocardial Injury in COVID-19

In patients with acute myocardial injury secondary to coronavirus disease-2019 (COVID-19), cardiovascular magnetic resonance imaging can identify the underlying pathology. We highlight a case of acute myocardial injury secondary to COVID-19, which demonstrated both epicardial vessel thrombosis and the recently described phenomenon of microvascular thrombosis. (Level of Difficulty: Advanced.

A 30-Year-Old Man With Primary Cardiac Angiosarcoma

A previously fit and well 30-year-old man presented with palpitations, fever, and pleuritic chest pain. Multimodality imaging and histopathology confirmed the diagnosis of primary cardiac angiosarcoma. We present the details of the presentation, diagnostic process using multimodality imaging, and clinical management. (Level of Difficulty: Beginner.

Cardiovascular magnetic resonance phenotyping of heart failure with mildly reduced ejection fraction

Aims The 2016 European Society of Cardiology Heart Failure Guidelines defined a new category: heart failure with mid-range ejection fraction (HFmrEF) of 40–49%. This new category was highlighted as having limited evidence and research was advocated into underlying characteristics, pathophysiology, and diagnosis. We used multi-parametric cardiovascular magnetic resonance (CMR) to define the cardiac phenotype of presumed non-ischaemic HFmrEF. Methods and results Patients (N = 300, 62.7 ± 13 years, 63% males) with a clinical diagnosis of heart failure with no angina symptoms, history of myocardial infarction, or coronary intervention were prospectively recruited. Patients underwent clinical assessment and CMR including T1 mapping, extracellular volume (ECV) mapping, late gadolinium enhancement, and measurement of myocardial blood flow at rest and maximal hyperaemia. Of 273 patients in the final analysis, 93 (34%) patients were categorized as HFmrEF, 46 (17%) as heart failure with preserved ejection fraction (HFpEF), and 134 (49%) as heart failure with reduced ejection fraction (HFrEF). Nineteen (20%) patients with HFmrEF had evidence of occult ischaemic heart disease. Diffuse fibrosis and hyperaemic myocardial blood flow were similar in HFmrEF and HFpEF, but HFmrEF showed significantly lower native T1 (1311 ± 32 vs. 1340 ± 45 ms, P < 0.001), ECV (24.6 ± 3.2 vs. 26.3 ± 3.1%, P < 0.001), and higher myocardial perfusion reserve (2.75 ± 0.84 vs. 2.28 ± 0.84, P < 0.001) compared with HFrEF. Conclusion Patients with HFmrEF share most phenotypic characteristics with HFpEF, including the degree of microvascular impairment and fibrosis, but have a high prevalence of occult ischaemic heart disease similar to HFrEF. Further work is needed to confirm how the phenotype of HFmrEF responds to medical therapy

4D Flow Cardiac MR in Primary Mitral Regurgitation

Background Four-dimensional-flow cardiac MR (4DF-MR) offers advantages in primary mitral regurgitation. The relationship between 4DF-MR-derived mitral regurgitant volume (MR-Rvol) and the post-operative left ventricular (LV) reverse remodeling has not yet been established. Purpose To ascertain if the 4DF-MR-derived MR-Rvol correlates with the LV reverse remodeling in primary mitral regurgitation. Study Type Prospective, single-center, two arm, interventional vs. nonintervention observational study. Population Forty-four patients (male N = 30; median age 68 [59–75]) with at least moderate primary mitral regurgitation; either awaiting mitral valve surgery (repair [MVr], replacement [MVR]) or undergoing “watchful waiting” (WW). Field Strength/Sequence 5 T/Balanced steady-state free precession (bSSFP) sequence/Phase contrast imaging/Multishot echo-planar imaging pulse sequence (five shots). Assessment Patients underwent transthoracic echocardiography (TTE), phase-contrast MR (PMRI), 4DF-MR and 6-minute walk test (6MWT) at baseline, and a follow-up PMRI and 6MWT at 6 months. MR-Rvol was quantified by PMRI, 4DF-MR, and TTE by one observer. The pre-operative MR-Rvol was correlated with the post-operative decrease in the LV end-diastolic volume index (LVEDVi). Statistical Tests Included Student t-test/Mann–Whitney test/Fisher's exact test, Bland–Altman plots, linear regression analysis and receiver operating characteristic curves. Statistical significance was defined as P < 0.05. Results While Bland–Altman plots demonstrated similar bias between all the modalities, the limits of agreement were narrower between 4DF-MR and PMRI (bias 15; limits of agreement −36 mL to 65 mL), than between 4DF-MR and TTE (bias −8; limits of agreement −106 mL to 90 mL) and PMRI and TTE (bias −23; limits of agreement −105 mL to 59 mL). Linear regression analysis demonstrated a significant association between the MR-Rvol and the post-operative decrease in the LVEDVi, when the MR-Rvol was quantified by PMRI and 4DF-MR, but not by TTE (P = 0.73). 4DF-MR demonstrated the best diagnostic performance for reduction in the post-operative LVEDVi with the largest area under the curve (4DF-MR 0.83; vs. PMRI 0.78; and TTE 0.51; P = 0.89). Data Conclusion This study demonstrates the potential clinical utility of 4DF-MR in the assessment of primary mitral regurgitation

Phenotyping hypertrophic cardiomyopathy using cardiac diffusion magnetic resonance imaging: the relationship between microvascular dysfunction and microstructural changes

Aims Microvascular dysfunction in hypertrophic cardiomyopathy (HCM) is predictive of clinical decline, however underlying mechanisms remain unclear. Cardiac diffusion tensor imaging (cDTI) allows in vivo characterization of myocardial microstructure by quantifying mean diffusivity (MD), fractional anisotropy (FA) of diffusion, and secondary eigenvector angle (E2A). In this cardiac magnetic resonance (CMR) study, we examine associations between perfusion and cDTI parameters to understand the sequence of pathophysiology and the interrelation between vascular function and underlying microstructure. Methods and results Twenty HCM patients underwent 3.0T CMR which included: spin-echo cDTI, adenosine stress and rest perfusion mapping, cine-imaging, and late gadolinium enhancement (LGE). Ten controls underwent cDTI. Myocardial perfusion reserve (MPR), MD, FA, E2A, and wall thickness were calculated per segment and further divided into subendocardial (inner 50%) and subepicardial (outer 50%) regions. Segments with wall thickness ≤11 mm, MPR ≥2.2, and no visual LGE were classified as ‘normal’. Compared to controls, ‘normal’ HCM segments had increased MD (1.61 ± 0.09 vs. 1.46 ± 0.07 × 10−3 mm2/s, P = 0.02), increased E2A (60 ± 9° vs. 38 ± 12°, P < 0.001), and decreased FA (0.29 ± 0.04 vs. 0.35 ± 0.02, P = 0.002). Across all HCM segments, subendocardial regions had higher MD and lower MPR than subepicardial (MDendo 1.61 ± 0.08 × 10−3 mm2/s vs. MDepi 1.56 ± 0.18 × 10−3 mm2/s, P = 0.003, MPRendo 1.85 ± 0.83, MPRepi 2.28 ± 0.87, P < 0.0001). Conclusion In HCM patients, even in segments with normal wall thickness, normal perfusion, and no scar, diffusion is more isotropic than in controls, suggesting the presence of underlying cardiomyocyte disarray. Increased E2A suggests the myocardial sheetlets adopt hypercontracted angulation in systole. Increased MD, most notably in the subendocardium, is suggestive of regional remodelling which may explain the reduced subendocardial blood flow