Mathematical Study of the Perturbation of Magnetic Fields Caused by Erythrocytes.

The purpose of this chapter is the mathematical study of the perturbation of a homogeneous static magnetic field caused by the embedding of a red blood cell. Analytical expressions for the magnetic potential and the magnetic strength vector are derived. From the obtained results, it emerges that the magnetic field inside the red blood cell is not uniform and the magnitude depends on the orientation of the erythrocyte. The expressions for the magnetic field quantities are significant in applications such as the magnetic resonance imaging and in the magnetic resonance spectroscopy.

Qualitative Differences Between the Semi-separable and the "Almansi-Type" Stokes Stream Function Expansions in the Study of Biological Fluids.

The creeping motion of a Newtonian fluid around particles simulating the relative motion of biological fluids such as blood plasma flow past red blood cells can be modeled through Stokes equations in spheroidal coordinates. By employing a stream function ψ, the irrotational and the rotational Stokes flow are described through a second- and a fourth-order elliptic-type partial differential equations: E2ψ = 0 and E4ψ = 0, respectively. Firstly, the complete set of the solution expansion has been obtained, in terms of particular combinations of Gegenbauer functions, in separable and semiseparable forms. Each of these terms, the so-called eigenflow, represents in a clearly and distinct way either rotational or irrotational type of flow. This information is of great value in the study of biofluids, as it may be correlated to characteristics observed in various diseases. Secondly, the Almansi-type solution is obtained as a kind of perturbation of the irrotational flow solution implying that no clear identification of the kind of flow is available. In the present manuscript, we demonstrate the advantages of the semiseparable form of solution and provide a reduction formula from the "Almansi-type" solution to the semiseparable one, indicating a way of revealing the hidden physical information.

Early Impact of the COVID-19 Pandemic on Congenital Heart Surgery Programs Across the World: Assessment by a Global Multi-Societal Consortium.

The coronavirus disease 2019 (COVID-19) pandemic currently gripping the globe is impacting the entire health care system with rapidly escalating morbidities and mortality. Although the infectious risk to the pediatric population appears low, the effects on children with congenital heart disease (CHD) remain poorly understood. The closure of congenital heart surgery programs worldwide to address the growing number of infected individuals could have an unintended impact on future health for COVID-19-negative patients with CHD. Pediatric and congenital heart surgeons, given their small numbers and close relationships, are uniquely positioned to collectively assess the impact of the pandemic on surgical practice and care of children with CHD. We present the results of an international survey sent to pediatric and congenital heart surgeons characterizing the early impact of COVID-19 on the care of patients with CHD.

A Microscale Mathematical Blood Flow Model for Understanding Cardiovascular Diseases.

The blood plasma flow through a swarm of red blood cells in capillaries is modeled as an axisymmetric Stokes flow within inverted prolate spheroidal solid-fluid unitary cells. The solid internal spheroid represents a particle of the swarm, while the external spheroid surrounds the spheroidal particle and contains the analogous amount of fluid that corresponds to the fluid volume fraction of the swarm. Analytical expansions for the components of the flow velocity are obtained by introducing a stream function ψ which satisfies the fourth-order partial differential equation E4ψ = 0. We assume nonslip conditions on the internal inverted spheroidal boundary which is also impermeable, while on the external spheroidal surface, we assume continuity of the tangential velocity component and nil vorticity. In order to solve the problem at hand, we employ the method of Kelvin inversion, under which, the initial problem, formulated in the inverted prolate spheroidal coordinates, is transformed to an equivalent one in the prolate spheroidal coordinates, where the solution space of the equation E4ψ = 0 is already known from our previously published work. The solution for the original problem is obtained by using the inverse Kelvin transformation and the effect of this transform to the Stokes operator (Dassios, IMA J Appl Math 74:427-438, 2009). Finally, the analytical solution for the stream function ψ is given through a series expansion of specific combinations of Gegenbauer functions of mixed order, multiplied by the Euclidean distance on the first and on the third power, in a so-called R-separable form.

Surgical Management of Aorto-Ventricular Tunnel. A Multicenter Study.

Aorto-ventricular tunnel (AoVT), a rare congenital anomaly, is a channel originating in the ascending aorta just above the sinotubular junction and leading to the cavity of the left ventricle (AoLVT), or, rarely, the right (AoRVT). This study reviews our collective 30-year experience with the surgical treatment of AoVT. Data were submitted by 15 participating centers on 42 patients who underwent correction of AoVT between 1987 and 2018. Of these, 36 had AoLVT, and 6 AoRVT. The tunnel originated above the right coronary sinus in 28 (77.8%) patients. For AoLVT, most operations were performed early (median age 25 days, range: 1 day-25 years). In contrast, AoRVT was diagnosed and repaired later (median age 6 years, range: 1 month-12 years). Surgically important coronary ostial displacement was common. Patch closure of the aortic orifice only was the commonest surgical repair for AoLVT (23 patients), while in AoRVT, both orifices or only the ventricular one was closed. Aortic valvar insufficiency, severe or moderate, coexisted in 11 (30.5%) patients with AoLVT, and aortic valvuloplasty was performed in 8, mainly due to aortic valve stenosis. Aortic valvar insufficiency at discharge ranged from trivial to mild in almost all patients. Early mortality was 7.14%, with 3 patients with AoLVT succumbing to cardiac failure. There were 2 early reoperations and 1 late death. AoVT is a rare malformation. AoLVT usually necessitates surgery in early life. AoRVT is rarer, diagnosed and repaired later in life. Surgical repair by patch closure, with concomitant aortic valve repair as needed, is associated with good results.

Late management of the aortic root after repair of tetralogy of Fallot: A European multicentre study.

OBJECTIVES: We sought to determine the indications, type, and outcomes of reoperations on the aortic root after repair of tetralogy of Fallot (TOF). METHODS: Eleven centers belonging to the European Congenital Heart Surgeons Association contributed to the data collection process. We included 36 patients who underwent surgical procedures on the aortic root, including surgery on the aortic valve and ascending aorta, between January 1975 and December 2017. Original diagnoses included TOF-pulmonary stenosis (n = 18) and TOF-pulmonary atresia (n = 18). The main indications for reoperation were aortic insufficiency (n = 19, 53%), aortic insufficiency and dilatation of the ascending aorta (n = 10, 28%), aortic root dilatation (n = 4, 11%), and ascending aorta dilatation (n = 3, 8%). RESULTS: The median age at reoperation was 30.4 years (interquartile range 20.3-45.3 years), and mechanical aortic valve replacement was the most common procedure performed. Five patients died early after reoperation (14%), and larger ascending aorta diameters were associated with early mortality (P = .04). The median age at the last follow-up was 41.4 years (interquartile range 24.5-51.6 years). Late death occurred in five patients (5/31, 16%). Most survivors (15/26, 58%) were asymptomatic at the last clinical examination (New York Heart Association, NYHA class I). The remaining patients were NYHA class II (n = 7) and III (n = 3). The most common symptoms were fatigue (n = 5), dyspnea (n = 4), and exercise intolerance (n = 3). CONCLUSIONS: Reoperations on the aortic root are infrequent but may become necessary late after TOF repair. The main indications for reoperation are aortic insufficiency, either isolated or associated with a dilatation of the ascending aorta. The surgical risk at reoperation was high and the presence of ascending aorta dilation is related to higher mortality.

Remarkably Still Repairable Large Aortopulmonary Window in an Adult Patient.

Aortopulmonary window (APW) is an abnormal congenital connection between the main pulmonary artery (MPA) and the ascending aorta, with intact aortic and pulmonary valves, leading to heart failure or, if not repaired early, to pulmonary vascular obstructive disease. We report the rare case of an asymptomatic adult with an unrestrictive APW, whose pulmonary arterial hypertension was remarkably still reversible, permitting successful repair.

Anomalous aortic origin of coronary arteries: Early results on clinical management from an international multicenter study.

BACKGROUND: Anomalous aortic origin of coronary arteries (AAOCA) is a rare abnormality, whose optimal management is still undefined. We describe early outcomes in patients treated with different management strategies. METHODS: This is a retrospective clinical multicenter study including patients with AAOCA, undergoing or not surgical treatment. Patients with isolated high coronary take off and associated major congenital heart disease were excluded. Preoperative, intraoperative, anatomical and postoperative data were retrieved from a common database. RESULTS: Among 217 patients, 156 underwent Surgical repair (median age 39 years, IQR: 15-53), while 61 were Medical (median age 15 years, IQR: 8-52), in whom AAOCA was incidentally diagnosed during screening or clinical evaluations. Surgical patients were more often symptomatic when compared to medical ones (87.2% vs 44.3%, p < 0.001). Coronary unroofing was the most frequent procedure (56.4%). Operative mortality was 1.3% (2 patients with preoperative severe heart failure). At a median follow up of 18 months (range 0.1-23 years), 89.9% of survivors are in NYHA ≤ II, while only 3 elderly surgical patients died late. Return to sport activity was significantly higher in Surgical patients (48.1% vs 18.2%, p < 0.001). CONCLUSIONS: Surgery for AAOCA is safe and with low morbidity. When compared to Medical patients, who remain on exercise restriction and medical therapy, surgical patients have a benefit in terms of symptoms and return to normal life. Since the long term-risk of sudden cardiac death is still unknown, we currently recommend accurate long term surveillance in all patients with AAOCA.

Left-Sided Reoperations After Arterial Switch Operation: A European Multicenter Study.

BACKGROUND: We sought to report the frequency, types, and outcomes of left-sided reoperations (LSRs) after an arterial switch operation (ASO) for patients with D-transposition of the great arteries (D-TGA) and double-outlet right ventricle (DORV) TGA-type. METHODS: Seventeen centers belonging to the European Congenital Heart Surgeons Association (ECHSA) contributed to data collection. We included 111 patients who underwent LSRs after 7,951 ASOs (1.4%) between January 1975 and December 2010. Original diagnoses included D-TGA (n = 99) and DORV TGA-type (n = 12). Main indications for LSR were neoaortic valve insufficiency (n = 52 [47%]) and coronary artery problems (CAPs) (n = 21 [19%]). RESULTS: Median age at reoperation was 8.2 years (interquartile range [IQR], 2.9-14 years). Seven patients died early after LSRs (6.3%); 4 patients with D-TGA (5.9%) and 3 patients with DORV TGA-type (25%) (p = 0.02). Median age at last follow-up was 16.1 years (IQR, 9.9-21.8 years). Seventeen patients (16%) required another reoperation, which was more frequent in patients with DORV- TGA type (4 of 9 [45%]) than in patients with D-TGA (13 of 95 [14%]). Late death occurred in 4 patients (4 of 104 [3.8%]). The majority of survivors were asymptomatic at last clinical examination (84 of 100 [84%]). CONCLUSIONS: Reoperations for residual LSRs are infrequent but may become necessary late after an ASO, predominantly for neoaortic valve insufficiency and CAPs. Risk at reoperation is not negligible, and DORV TGA-type anatomy, as well as procedures on the coronary arteries, were significantly associated with a higher morbidity and a lower overall survival. Recurrent reoperations after LSRs may be required.

Translation of two aggregated low-density lipoproteins within blood plasma: a mathematical model.

Arteriosclerosis is a disease in which the artery walls get thicker and harder. Atherosclerosis is a specific form of arteriosclerosis which allows less blood to travel through the artery and increases blood pressure. Low-density lipoproteins (LDLs) and their ability to aggregate are important in atherosclerosis. In the present study we develop a mathematical model that describes the translation of two aggregated LDSs through blood plasma. We model the two aggregated LDLs as an inverted oblate spheroid and the flow as a creeping steady incompressible axisymmetric one. The mathematical tools that we used are the Kelvin inversion and the semi-separation of variables in the spheroidal coordinate systems. The stream function is given as a series expansion of even order terms of combinations of Gegenbauer functions of angular and radial dependence. The analytical solution is expected to give insight into the study of the various chemical precipitation methods used for the precipitation of lipoproteins, as this is the first step for the measurement of their concentration within blood plasma.