Theory - Biofluid Dynamics

Introduction to biofluid dynamics

Biological fluid mechanics (or biofluid mechanics) is the study of the motion of biological fluids in any possible context (e.g. blood flow in arteries, animal flight, fish swimming...). Focusing on the human body, there are many organs in whose functioning involves fluid motion:

Ex.

• Blood circulation: flow in arteries and in veins, in the microcirculation
• Air flow in the respiratory system
• Flow in the eye: flow in the cornea, of the aqueous or of the vitreous body
• Flow in the ureter
• Nerve circulation in the kidney

Biological fluid mechanics is useful for:

• Pure physiology: understanding how animals, and in particular human, work
• Pathophysiology: understanding why they might go wrong; in other words understanding the origins and development of diseases
• Diagnosis: recognising disease from possibly non-traumatic measurements
• Cure: providing support to surgery and to the design of prosthetic devices

Fundamentals of biofluid mechanics are necessary in different engineering approaches:

• Monitoring and data interpretation
• Modelling
• Design

There are some key features which characterise physiological flows:

• Pulsatility: in most cases physiological flows are highly unsteady and are often pulsatile (e.g. flow in the systemic arteries or in the respiratory system)
• Complex geometries: typically physiological flows take place in very complex geometries. In order to study the problems by analytical means it is therefore necessary to idealise the geometry in a suitable manner. It is a research challenge of recent years to perform numerical simulations on real geometries
• Deformability: not only the geometry of the flow domain might be complex, but it also often varies in time. This typically induces great complication in the mathematical analysis; often the problem to be solved is effectively a fluid-fluid interaction
• Low Reynolds number flows: in many cases of physiological interest (but by no means always) the Reynolds number of the flow is fairly low and this allows simplifying the equations

Introduction to biofluid dynamics

Biological fluid mechanics (or biofluid mechanics) is the study of the motion of biological fluids in any possible context (e.g. blood flow in arteries, animal flight, fish swimming...). Focusing on the human body, there are many organs in whose functioning involves fluid motion:

Ex.

• Blood circulation: flow in arteries and in veins, in the microcirculation
• Air flow in the respiratory system
• Flow in the eye: flow in the cornea, of the aqueous or of the vitreous body
• Flow in the ureter
• Nerve circulation in the kidney

Biological fluid mechanics is useful for:

• Pure physiology: understanding how animals, and in particular humans, work
• Pathophysiology: understanding why they might go wrong; in other words understanding the origin and development of diseases
• Diagnosis: recognising disease from possible non-traumatic measurements
• Cure: providing support to surgery and to the design of prosthetic devices

Fundamentals of biofluid mechanics are necessary in different engineering approaches:

• Monitoring and data interpretation
• Modelling
• Design

There are some key features which characterise physiological flows:

• Pulsatility: in most cases physiological flows are highly unsteady and are often pulsatile (e.g. flow in the systemic arteries or in the respiratory system)
• Complex geometries: typically physiological flows take place in very complex geometries. In order to study the problems by analytical means it is therefore necessary to idealise the geometry in a suitable manner. It is a research challenge of recent years to perform numerical simulations on real geometries
• Deformability: not only the geometry of the flow domain might be complex, but it also often varies in time. This typically induces great complication in the mathematical analysis; often the problem to be solved is effectively a solid-fluid interaction
• Low Reynolds number flows: in many cases of physiological interest (but by no means exclusively) the Reynolds number of the flow is fairly low and this allows simplifying the equations

Basic notions of fluid mechanics

The continuum approach

Fluids (liquids, gases ...) are composed of particles (molecules). Each molecule is composed of a central nucleus surrounded by a cloud of electrons. Some typical dimensions are given in the following table

In most applications of fluid mechanics, the typical scale under consideration, L, is much larger than the spacing between molecules, l. In this case we assume the fluid occupies every point in space and each