Hemodynamics

Key takeaways

Hemodynamics belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Hemodynamics to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Hemodynamics from memory before moving on to harder problems.

Reference excerpt

Hemodynamics or haemodynamics are the dynamics of blood flow. The circulatory system is controlled by homeostatic mechanisms of autoregulation, just as hydraulic circuits are controlled by control systems. The hemodynamic response continuously monitors and adjusts to conditions in the body and its environment. Hemodynamics explains the physical laws that govern the flow of blood in the blood vessels. Blood flow ensures the transportation of nutrients, hormones, metabolic waste products, oxygen, and carbon dioxide throughout the body to maintain cell-level metabolism, the regulation of the pH, osmotic pressure and temperature of the whole body, and the protection from microbial and mechanical harm. Blood can behave as a non-Newtonian fluid, and is most commonly studied using rheology. Because blood vessels are not rigid tubes; classic hydrodynamics based on the use of classical viscometers are not capable of explaining haemodynamics. The study of the blood flow is called hemodynamics, and the study of the properties of the blood flow is called hemorheology.

Blood

Blood is a complex liquid. Blood is composed of plasma and formed elements. The plasma contains 91.5% water, 7% proteins and 1.5% other solutes. The formed elements are platelets, white blood cells, and red blood cells. The presence of these formed elements and their interaction with plasma molecules are the main reasons why blood differs so much from ideal Newtonian fluids.

Viscosity of plasma Normal blood plasma behaves like a solid suspended in fluid and blood is modelled as a Newtonian fluid at normal physiological flow rates. Typical values for the viscosity of normal human plasma at 37 °C is 1.4 mN·s/m2. The viscosity of normal plasma varies with temperature in the same way as does that of its solvent water; a 3 °C change in temperature in the physiological range (36.5 °C to 39.5 °C)reduces plasma viscosity by about 10%.

Osmotic pressure of plasma The osmotic pressure of solution is determined by the number of particles present and by the temperature. For example, a 1 molar solution of a substance contains 6.022×1023 molecules per gram of that substance and at 0 °C it has an osmotic pressure of 2.27 MPa (22.4 atm). The osmotic pressure of the plasma affects the mechanics of the circulation in several ways. An alteration of the osmotic pressure difference across the membrane of a blood cell causes a shift of water and a change of cell volume. The changes in shape and flexibility affect the mechanical properties of whole blood. A change in plasma osmotic pressure alters the hematocrit, that is, the volume concentration of red cells in the whole blood by redistributing water between the intravascular and extravascular spaces. This in turn affects the mechanics of the whole blood.

Red blood cells The red blood cell is highly flexible and biconcave in shape. Its membrane has a Young's modulus in the region of 106 Pa. Deformation in red blood cells is induced by shear stress. When a suspension is sheared, the red blood cells deform and spin because of the velocity gradient, with the rate of deformation and spin depending on the shear rate and the concentration. This can influence the mechanics of the circulation and may complicate the measurement of blood viscosity. It is true that in a steady state flow of a viscous fluid through a rigid spherical body immersed in the fluid, where we assume the inertia is negligible in such a flow, it is believed that the downward gravitational force of the particle is balanced by the viscous drag force. From this force balance the speed of fall can be shown to be given by Stokes' law

U s = 2 9 ( ρ p − ρ f ) μ g a 2 {\displaystyle U_{s}={\frac {2}{9}}{\frac {\left(\rho _{p}-\rho _{f}\right)}{\mu }}g\,a^{2}}

Where a is the particle radius, ρp, ρf are the respectively particle and fluid density μ is the fluid viscosity, g is the gravitational acceleration. From the above equation we can see that the sedimentation velocity of the particle depends on the square of the radius. If the particle is released from rest in the fluid, its sedimentation velocity Us increases until it attains the steady value called the terminal velocity (U), as shown above.

… excerpt ends here. Continue reading the full article.

Illustrations

Hemodynamics: Laser Doppler imaging reveals retinal blood flow — Laser Doppler imaging reveals retinal blood flow

Worked examples

Example 1 — a first encounter with Hemodynamics

Start with the simplest possible case. Write down what Hemodynamics claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Hemodynamics before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Hemodynamics ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Hemodynamics

In research: Hemodynamics appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Hemodynamics in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Hemodynamics is common in secondary-school and first-year university syllabi. It links to neighbouring topics Blood, Cardiovascular physiology, Computational fluid dynamics, so understanding it makes those chapters shorter.
In everyday life: Look for Hemodynamics outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Hemodynamics in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Hemodynamics means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Hemodynamics out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hemodynamics in simple terms?

Hemodynamics or haemodynamics are the dynamics of blood flow. The circulatory system is controlled by homeostatic mechanisms of autoregulation, just as hydraulic circuits are controlled by control systems.

Why does Hemodynamics matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Hemodynamics?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Hemodynamics.