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Related Concept Videos

The Number e as a Limit01:29

The Number e as a Limit

The number e is a fundamental constant in calculus, playing a central role in describing continuous change, particularly exponential growth. It is most naturally defined through its relationship with the natural logarithm, which is the inverse of the exponential function with base e. This relationship allows e to be characterized using basic principles of differentiation rather than as an arbitrary numerical constant.A key property of the natural logarithm function, ln x, is that its derivative...
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In calculus, limit laws serve as foundational tools for evaluating the behavior of functions as inputs approach specific values. Among these, the laws concerning quotients, powers, and roots are particularly useful in breaking down complex expressions.The Quotient Law allows the limit of a division between two functions to be calculated by dividing their individual limits, provided the limit of the denominator exists and is not zero. For example,The Power Law states that the limit of a function...
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When observing how a curve behaves near a specific point along the horizontal axis, there are cases where the curve’s height increases or decreases without limit as the position draws closer to that point. The curve does not settle at any particular value; instead, the values grow more extreme—upward or downward—the nearer they get. No defined value exists exactly at that location, yet the surrounding behavior becomes more dramatic, indicating a sharp change in direction.The values may rise...
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The function that decreases as the input becomes very large provides a clear example of how mathematical functions can behave at extreme values. When the input increases continuously, the output becomes smaller and smaller, getting closer to a particular fixed value. Although the output never actually reaches this value, it moves nearer to it without limit. This behavior is a fundamental concept in understanding how functions behave as the input grows indefinitely. The graphical representation...

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Quadruple-Checkerboard: A Modification of the Three-Dimensional Checkerboard for Studying Drug Combinations
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Don't stop at two.

John A Purvis1, Vincent Kennedy, Albert J McNeill

  • 1Cardiac Unit, Altnagelvin Hospital, Western HSC Trust, Glenshane Road, Londonderry, BT47 6SB, UK. john.purvis@btinternet.com

The International Journal of Cardiovascular Imaging
|December 30, 2009
PubMed
Summary
This summary is machine-generated.

A rare partial Shone complex case presented with a parachute mitral valve causing left ventricular outflow tract obstruction. This highlights the importance of searching for multiple obstructions in congenital heart disease.

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Area of Science:

  • Cardiology
  • Medical Diagnostics
  • Congenital Heart Disease

Background:

  • Routine echocardiography in a patient with a history of coarctation repair.
  • Identification of a bicuspid aortic valve with a significant left ventricular outflow tract (LVOT) gradient.

Observation:

  • Redundant anterior mitral valve leaflet noted on echocardiogram.
  • Transesophageal echo revealed thickened chordae tendineae inserting into a single papillary muscle, consistent with a parachute mitral valve.
  • Anterior systolic motion of redundant mitral chordae caused significant LVOT obstruction.

Findings:

  • Diagnosis of partial Shone complex established.
  • Significant LVOT obstruction secondary to parachute mitral valve and redundant chordae.

Implications:

  • Partial Shone complex can present subtly in adults.
  • Combined aortic coarctation and bicuspid aortic valve necessitate a thorough search for additional obstructive lesions.
  • Surgical intervention for mitral and potentially aortic valve may be required.