Montgomery Reduction Algorithm for Modular Multiplication Using Low-Weight Polynomial Form Integers

At low weight fractions, many surfactant and biological amphiphiles form dispersions of lamellar liquid crystalline liposomes in water. Amphiphile molecules tend to align themselves in parallel bilayers which are free to bend. Bilayers must form closed surfaces to separate hydrophobic and hydrophilic domains completely. Continuum theory of liquid crystals requires that the constant spacing of bilayer surfaces be maintained except at singularities of no more than line extent. Maxwell demonstrated that only two types of closed surfaces can satisfy this constraint: concentric spheres and Dupin cyclides. Dupin cyclides (Figure 1) are parallel closed surfaces which have a conjugate ellipse (r1) and hyperbola (r2) as singularities in the bilayer spacing. Any straight line drawn from a point on the ellipse to a point on the hyperbola is normal to every surface it intersects (broken lines in Figure 1). A simple example, and limiting case, is a family of concentric tori (Figure 1b).To distinguish between the allowable arrangements, freeze fracture TEM micrographs of representative biological (L-α phosphotidylcholine: L-α PC) and surfactant (sodium heptylnonyl benzenesulfonate: SHBS)liposomes are compared to mathematically derived sections of Dupin cyclides and concentric spheres.

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A Novel Approach: Trans-ascending Aorta Balloon Aortic Valvuloplasty via Sternotomy for Treating Severe Valvular Aortic Stenosis in a Low-Weight Infant

The Heart Surgery Forum ◽

10.1532/hsf98.2013277 ◽

2014 ◽

Vol 17 (1) ◽

pp. 25 ◽

Cited By ~ 1

Author(s):

Lei Gao ◽

Qin Wu ◽

Xinhua Xu ◽

Tianli Zhao ◽

Wancun Jin ◽

...

Keyword(s):

Aortic Stenosis ◽

Transesophageal Echocardiography ◽

Severe Aortic Stenosis ◽

Ascending Aorta ◽

Balloon Aortic Valvuloplasty ◽

Congenital Aortic Stenosis ◽

Novel Approach ◽

Low Weight ◽

Aortic Valvuloplasty ◽

Peak Gradient

Background: Severe congenital aortic stenosis in infants is a life-threatening congenital heart anomaly that is typically treated using percutaneous balloon aortic valvuloplasty.Methods: The usual route is the femoral artery under radiographic guidance. However, this procedure may be limited by the small size of the femoral artery in low-weight infants. An infant weighing only 7 kg with severe aortic stenosis (peak gradient was 103 mmHg) was successfully treated with a novel approach, that is trans-ascending aorta balloon aortic valvuloplasty guided by transesophageal echocardiography.Results: The patient tolerated the procedure well, and no major complications developed. After the intervention, transesophageal echocardiography indicated a significant reduction of the aortic valvular peak gradient from 103 mmHg to 22 mmHg, no aortic regurgitation was found. Eighteen months after the intervention, echocardiography revealed that the aortic valvular peak gradient had increased to 38 mmHg and that still no aortic regurgitation had occurred.Conclusions: In our limited experience, trans-ascending aorta balloon aortic valvuloplasty for severe aortic stenosis under transesophageal echocardiography guidance effectively reduces the aortic peak gradient. As this is a new procedure, long-term follow up and management will need to be established. It may be an alternative technique to treat congenital aortic stenosis in low-weight patients.

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