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Vascular tortuosity: a mathematical modeling perspective.

Leith Hathout1, Huy M Do

  • 1Department of Biology, Stanford University, Palo Alto, USA. lhathout@stanford.edu

The Journal of Physiological Sciences : JPS
|January 19, 2012
PubMed
Summary
This summary is machine-generated.

Vascular tortuosity, the winding of blood vessels, follows physical principles. A new mathematical model suggests vessels minimize average curvature, potentially distinguishing normal from diseased states.

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Area of Science:

  • Biophysics
  • Mathematical Biology
  • Vascular Biology

Background:

  • Vascular tortuosity is common but lacks mathematical models.
  • The uniform shape of tortuous vessels suggests underlying physical principles.
  • Distinguishing physiologic from pathologic tortuosity is clinically relevant.

Purpose of the Study:

  • To develop a mathematical model for vascular tortuosity based on optimality principles.
  • To investigate if vascular shape minimizes average curvature.
  • To assess the model's potential in differentiating normal from abnormal vascularity.

Main Methods:

  • Utilized the calculus of variations to formulate a tortuosity model.
  • The model minimizes average curvature per unit length.
  • Applied the model to vascular curves from normal subjects and a patient with Fabry's disease.

Main Results:

  • The mathematical model accurately describes normal vascular tortuosity.
  • Vessel curves in normal vasculature align with the principle of minimized average curvature.
  • The model shows promise in distinguishing normal from abnormal tortuosity.

Conclusions:

  • Blood vessels appear to follow optimality principles, minimizing average curvature.
  • This model offers a quantitative approach to understanding vascular shape.
  • The developed model may aid in diagnosing diseases associated with abnormal vascular tortuosity.