Understanding Red Blood Cell Shape: Impact on Hemodynamics | Hemodynamic Help

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SUMMARY

The discussion focuses on the shape of red blood cells (RBCs) and its implications for hemodynamics. It establishes that a red blood cell has a fixed volume of 98 μm³ and explores the geometric properties of spherical versus non-spherical shapes. The spherical shape would require a minimum pore size for passage, while the actual shape of RBCs allows for deformation, enhancing their ability to navigate through smaller vessels. The advantages of non-spherical RBCs include improved flexibility and surface area for gas exchange.

PREREQUISITES
  • Understanding of basic geometry, particularly volume and surface area calculations.
  • Familiarity with red blood cell anatomy and function.
  • Knowledge of hemodynamics and blood flow mechanics.
  • Ability to solve cubic equations numerically.
NEXT STEPS
  • Research the mathematical properties of spheres and their applications in biology.
  • Learn about the mechanics of blood flow and the role of red blood cell shape in circulation.
  • Study the deformation mechanics of biological cells under stress.
  • Explore the implications of red blood cell shape on oxygen delivery and overall physiology.
USEFUL FOR

Students in biology or biomedical engineering, researchers studying hemodynamics, and healthcare professionals interested in the physiological implications of red blood cell morphology.

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Homework Statement



The red blood cell is very oddly shaped, and it is natural to wonder why it
is not spherical. This question should tell you the answer. Since the body
requires a certain minimum amount of hemoglobin in the blood (and hence a
certain minimum red cell volume), let us consider the red cell volume to be
fixed at 98 μm3.

(a) If the red blood cell were spherical, what is the smallest pore that it could
fit through? Assume that the red blood cell membrane will rupture if
stretched (a very good approximation) and remember that a sphere is the
geometrical object having minimum surface area for a given volume.

(b) Now consider the real shape of a red blood cell and allow the cell to
deform as it passes through a pore of radius R (Fig. 3.18). Assume that
the red blood cell is cylindrical with hemispherical ends. Taking cell
membrane area as 130 μm2, what is the minimum R value? You will get
a cubic equation for R; solve it numerically.

(c) Why is it advantageous to have non-spherical red blood cells?


Homework Equations



The Attempt at a Solution


Can't even begin since professor didn't teach anything..
 
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If you don't follow the directions given in the problem, you won't get much help here.

You can't blame the professor if you give up without doing anything.
 
FreshlySqueez said:
(a) If the red blood cell were spherical, what is the smallest pore that it could fit through? Assume that the red blood cell membrane will rupture if stretched (a very good approximation) and remember that a sphere is the geometrical object having minimum surface area for a given volume.

You need to look up the formula for the volume of a sphere.
 

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