V5

• Transport of oxygen and nutrients

• Removal of waste products

• Exchange of messenger substances

• Immune system

• Regulation of body temperature

• Conduct blood away from the heart

• Generally round

• High pressure

• Thick walls

• Not very elastic

• High oxygen concentration in systemic circulation

• Low oxygen concentration in pulmonary circulation

• Do not contain valves

• Conduct blood towards the heart

• Irregularly shaped

• Low pressure

• Thin walls

• Very elastic

• Low oxygen concentration in systemic circulation

• High oxygen concentration in pulmonary circulation

• Contain valves

• Connection between arteries and veins

• Exchange of materials between the blood and tissue cells

• Size of capillary bed depends on tissue type

• Diameter: ⌀ 8 µm (Size of erythrocyte)

• Wall thickness: 0.5 µm

• Consists of a fluid (lymph), lymphatic vessels and lymph nodes

• Drainage system for returning interstitial tissue fluid (interstitielle Gewebeflüssigkeit) and inflammatory cells (Entzündungszellen) to the blood

• Lymph nodes filter and provide immunologic surveillance of the lymph, its cells, and the foreign matter it contains

• Thin walls

• Located near capillary beds

• Contain valves

• Transport medium pumped by the heart throughout the body

• Transports oxygen and nutrients to the cells

• Carries away carbon dioxide and other waste products

• Regulatory functions enables adaptation to changing conditions of life

• Monitors the heart’s electrical rhythm

• Delivers controlled electrical impulses when needed to restore normal heart activity

• Battery lasts about 10 years

• 3 configurations

• Single Chamber

• Dual Chamber

• Biventricular

• Subcutaneous implantable cardioverter defibrillator (S-ICD)

  • unlike traditional ICDs, the S-ICD lead is placed just under the skin, leaving the heart and veins untouched

  • Con: Bigger than ICDs

• Leadless pacemakers

  • self-contained capsule that includes the battery, generator, and pacing electrodes

  • implanted percutaneously (through the skin) through the femoral vein

  • Con: currently only single-chamber RV pacing

Newtonian fluids:

• Linear relationship between applied force (τ = shear stress) and flow (𝛾ሶ = shear rate)

• 𝜏 = 𝜂 ⋅ 𝛾ሶ

• Water and oil exhibit Newtonian flow behavior

Non-Newtonian fluids:

• Non-linear relationship between applied force and flow.

• Heterogeneous materials or biological fluids consisting of multiple materials

At constant temperature and flow conditions, the following variables are relevant for the rheological properties of blood:

1) Plasma viscosity: Cell-free part of the blood

2) Hematocrit: Red blood cells (Erythrocytes), Red cell plasticity

3) Red blood cell aggregation: Clumping of blood → Significantly determines blood viscosity

• Shear dependent viscosity

  • Non-Newtonian fluid at low shear rates

  • Newtonian fluid at high shear rates

• At low shear rates

  • RBCs tend to aggregate (Rouleaux)

  • Aggregation determines viscosity at low shear rates

• At high shear rates

  • RBC orient with the flow streamlines and behave like droplets

• describes the decrease of hematocrit - lower average concentration of RBCs - in a small tube r < 500 µm (capillary)

• whole blood separates into a cell-free plasma layer along the tube wall and enriched central core

• RBCs at the center move faster than the plasma at the tube wall

• Fåhræus–Lindqvist effect describes the reduction of viscosity until the deformability limit of RBCs

• Fåhræus effect contributes to the Fåhræus– Lindqvist effect

  • plasma cell-free area functions as a sliding layer (lower viscosity)

  • plasma cell-free area about 3 -5 µm thick

  • reduction of the internal friction between RBCs

• Decrease of blood viscosity as the diameter of a vessel decreases (Fåhræus–Lindqvist effect) • Blood viscosity approaches plasma viscosity at a vessel diameter around 7-10 µm (size of RBC)

• Further deacrease in vessel diameter increases the viscosity dramatically

  • the tubes become too narrow for the RBCs to squeeze through (deformability limit)

• Multi-profile flow with grater vessel diameter

  • RBCs travel in different streamlines with different velocities

  • this irregular movement increases internal friction between RBCs and vessel wall leading to higher viscosities

• mesh-free methods that employ a set of finite number of discrete particles to represent the state of a flow system and to record the evolution of the system (i.e., their positions and velocities)

• Pro: Simulation of complex structures like flexible RBCs

• Con: high computational costs

• The Fahraeus effect and the Fahraeus– Lindqvist effect serve as a standard validation test for blood flow models

• mesoscopic model

• the whole computational domain is discretized into a set of particles

  • particles may be considered as a cluster of particles

• different DPD particles are employed to distinguish different components in the computational domain

  • e.g., RBC membrane, internal fluid, suspending fluid, wall

• particles move according to Newton’s second law

• mesoscopic model

• a hybrid mesh-particle method

• the fluid is modeled as a set of fictitious particles, and such particles undergo consecutive propagations and collision processes over a discrete lattice mesh

• usually the immersed boundary method (IBM) is used to handle the fluid-RBC interaction

• macroscopic model

• a kernel function is used to discretize the whole computational domain into a set of particles

• each particle has a spatial distance, called the smoothing length, over which its physical properties are given by the kernel function

• different particles are employed to distinguish different components in the computational domain (like DPD)

• particles move according to Newton’s second law (like DPD)

• Haemoglobin forms stiff rods inside the red blood cells, making them rigid and inflexible

• Loss of flexibility leads to blockage of vessels

• Sickle cells die much faster than healthy ones, typically lasting 10- 20 days, causing a shortage of red blood cells resulting in shortage of oxygen supply

• The wall of the artery develops abnormalities that lead to narrowing

  • The narrowing of arteries limits the flow of oxygen-rich blood to parts of the body

• It can result in coronary artery disease, stroke, peripheral artery disease, or kidney problems, depending on which arteries are affected

• It is the number one cause of death and disability in the developed world

• prevailing vascular disorder

• formation of a blood clot inside a blood vessel

  • blood has to be diverted over and around the clot leading to an increase of flow velocity

• A clot, or a piece of the clot, that breaks free and begins to travel around the body is known as an embolus

  • embolus can lead to blockage and hence to a disturbance of blood supply

• Thrombosis-on-Chip that models human response in an engineered living microenvironment

• In vitro study to understand clogging and to predict human response in drug delivery processes

1) laminar or turbulent flow : Re < 2000: laminar, Re > 2000: turbulent +

2) compressible or incompressible

3) viscous or non-viscous

4) rotational (vortices) or irrotational

5) steady (constant in time) or pulsatile (with pulsing changes)

• Bernoulli’s equation assumes ideal, non-viscous fluid

• Viscosity is the friction during flow and causes the pressure to drop during flow

• To maintain flow in a tube a pressure difference is needed

• Blood pressure is usually given as gauge pressure (pressure relative to atmospheric pressure): 𝑃𝑔𝑎𝑢𝑔𝑒 = 𝑃𝑎𝑏𝑠 − 1 𝑎𝑡𝑚

• Blood pressure is measured in arteries using a sphygmomanometer (veins do not have sufficient pressure to be easily detected)

• Predicts thickness of branches in biological transport networks

  • cardiovascular system

  • respiratory system

• Basic physical principle

• Minimizes energy needed for transport and maintenance processes

  • Loss via shear force -> ideal volume as large as possible

  • Loss via metabolic maintenance -> ideal volume as small as possible

• Derivation through Hagen-Poiseuille and continuity equation

• Advancement of Murray‘s law

• Considers blood as non-newtonian fluid

• Optimizes vessel diameter according to oxygen delivery instead of maintenance metabolism