Theory - Bio-fluid Dynamics (Part II)

The cardiovascular system: blood rheology

In large animals, transport of material from different parts of the body involves fluid flowing along and across the walls of a system of tubes.

The most studied tube system in biofluidics is the mammalian cardiovascular system; the fluid flowing in such a system is blood.

Blood

There are approximately 5 liters of blood in an average human being and the blood volume is regulated by the kidneys.

Blood has several different functions:

• Carries oxygen and nutrients to metabolically active tissues
• Returns carbon dioxide to the lungs
• Delivers metabolic end-products to the kidneys
• Provides a buffering reservoir to control the pH of bodily fluids
• Serves as an important locus for the immune system
• Transports heat, contributing to maintain a constant temperature throughout the body

In the present section we will be concerned with blood rheology, i.e. the way in which forces are generated in the blood and response to a given kinematic state.

In order to understand the rheological behavior of blood we need to review its composition.

Blood consists of a suspension of particles (formed elements) floating in a fluid medium (plasma). The formed elements constitute approximately 46% of the total blood volume.

Being the plasma mainly composed by water, the plasma behavior is similar to that of water.

The 2^nd component in concentration is the albumin, which has a role on the interaction between plasma and the red blood cells.

The cardiovascular system: blood rheology

As large animals, transport of material from different parts of the body involves fluid flowing along and across the tubes of a system of tubes.

The most studied tube system in biomechanics is the mammalian cardiovascular system, the fluid flowing in such a system is blood.

Blood

There are approximately 5 liters of blood in an average human being and the blood volume is regulated by the kidneys.

Blood has several different functions:

• Carries oxygen and nutrients to metabolically active tissues
• Returns carbon dioxide to the lungs
• Delivers metabolic end-products to the kidneys
• Provides a buffering reservoir to control the pH of body fluids
• Serves as an important locus for the immune system
• Transports heat, contributing to maintain a constant temperature throughout the body

In the present section, we will be concerned with blood rheology, i.e., the way in which tensions are generated in the blood and response to a given kinematic state.

In order to understand the rheological behaviour of blood we need to review its composition.

Blood consists of a suspension of particles (for. elements) floating in a fluid medium (plasma). The formed elements constitute approximately 46% of the total blood volume.

Being the plasma mainly composed of water, the plasma behaviour is similar to that of water.

The 2^nd component in concentration is the albumin, which has a role on the interaction between plasma and the red blood cells.

Formed elements

The formed elements mainly consist of the following bodies:

• Red cells (→ erythrocytes)
  • Are the means of delivering oxygen to the body tissues via the blood flow
  • They take up oxygen in the lungs or gills and release it in the microcirculation
  • They have no nucleus
  • They are easily deformable
• White cells (→ leukocytes)
  • They play an important role in the immune response as they defend the body against both infectious diseases and external materials
  • There are various different types of leukocytes
• Platelets
  • Are small cytoplasmic bodies derived from cells in the bone marrow
  • They circulate in the blood and are involved in blood clotting
  • Like red cells, platelets have no nucleus
  • If the number of platelets is too low, excessive bleeding can occur, however if the number is too high, blood clots can form

The percentage of blood cells present in normal blood is much larger than the percentage of white cells and platelets → this implies that the mechanical behavior of the formed elements is dominated by red cells.

Hence the volume fraction of red blood cells is extremely important for blood rheology (and also for physiological characteristics of blood), such important index is given by hematocrit H which is defined as

1. Volume of formed elements in blood = volume of red blood cells
2. Total blood volume = total blood volume

Normal values of the hematocrit are around 0.45 (45%).

• Individual red blood cells are shaped like biconcave discs and has a scale of
  • d ≈ 1 - 10 μm
  • Thickness μ = 1μ
  • Diameter/thickness ≈ 6-2

The cytoplasm of red cells has a viscosi