Biofluid dynamics

Reynold's number

dimensionless quantity that helps predict fluid flow patterns (ratio between inertial and viscous forces)

low Reynold's number

flow is dominated by laminar flow (viscous forces dominate)

high reynold's number

inertial forces dominate, turbulent flow

Where would you find small Reynold's numbers?

capillary, cochlea, vitreous humor (eye), lymphatic system

stoke's flow

fluid flow where inertial forces are very small compared to viscous forces, characterized by a very low Reynold's number

Womersley number

non-dimensional frequency, ratio between effects of unsteadiness and viscosity

small womersley number

unsteadiness is not important and solutions become parabolas, they vary in magnitude but not in shape

large womersley number

shape of the profiles is not parabolic, unsteadiness wins/is more important

which term of the navier stokes equation can be dropped for small womersley numbers?

unsteady term (rho du/dt) b/c small womersley numbers mean that unsteadiness is negligible

hematocrit

volumetric concentration of red blood cells in whole blood. Tube hematocrit is lower than discharged hematocrit

hemolysis

destruction of RBCs

Thrombosis

formation of blood clots; if these clots break off or get large enough, they can lead to events like stroke

Ways thrombosis can be triggered

shear-induced platelet activation: body thinks it's in trouble b/c blood shear cuts into the veins/arteries (turbulent blood flow) and sends platelets which block

shear-induced platelet activation

prolonged exposure to shear stresses above 10Pa

Fahraeus lindquist effect

as vessel diameter decreases (<0.3mm), viscosity of blood decreases b/c axial concentration of RBCs and cell-depleted layer close to the vessel wall

Dynamic viscosity

fluid's resistance to flow when external force is applied

pulsatile flow in large arter

flow lags behind pressure pulse

If pulsatile flow goes up an pressure is held constant

amplitude of flow rate decreases

dean vortices

secondary flow perpendicular to main axis, skewed axial velocity profile, increased wall shear stress at outer wall, if De > 65-75 you get dean vortices, more normal for larger pipes I believe

Distensibility

ability of a vessel to expand or stretch in response to changes in pressure (metric of stiffness of the blood vessels)- softer vessel walls would have higher distensibility

CO equation

CO = SV * HR

Most significant drop in BP

arterioles

Blood platelets

thrombocytes, central role in blood coagulation

how are blood platelets activated

damage of endothelium, excessive mechanical stress

thromogenicity

ability of material to promote blood clot formation

newtonian fluid

viscosity is unaffected by shear rate

apparent viscosity

derived from Poiseuille's (laminar, steady flow of a newtonian fluid)

shear-thinning fluid

viscosity decreases with increasing shear rate

Reverse fahraeus lindqvist effect

in very small capillaries (<5 micrometers), the apparent viscosity increases again b/c RBCs have to deform heavily to fit through capillary

Left ventricle

drives systemic circulation, oxygenated blood

right ventricle

drives pulmonary circulation, non-oxygenated blood

order of heart valves used

Tricuspid (filling right side), pulmonary valve (ejection right side), mitral valve (filling left side), aortic valve (ejection left side)

Mitral valve

two leaflets, located between left atrium and left ventricle, open during diastole (filling LV), closed during systole

aortic valve

three cusps, located between LV and aorta, systolic ejection of blood into aorta, open during systole, closed during diastole

Layers of the arteries (out —> in)

tunica adventita, tunica media, tunica intimav

veins

more veins than arteries, more compliant than arteries, many veins contain valves that prevent backflow

transmural pressure

pressure difference across the wall of a blood vessel

How does a cochlear implant work

1. sound processor captures sound and converts it into digital code

2. sound processor transmits the digital coded sound through the coil and to the implant under the skin

3. the implant converts the digitally coded sound to electrical signals and sends them along the electrode array, which is positioned in the cochlea

   1. the implant’s electrodes stimulate the cochlea’s hearing nerve fibers, which relay sound signals to the brain to produce hearing sensations

Two sensory systems in the inner ear

hearing sense (cochlea) and balance sense (vestibular system)

two fluid spaces in the inner ear

endolymph and perilymph (density and viscosity like water)

Outer hair cells

mechanically stimulated by a relative motion between the basilar membrane and the tectorial membrane

only OHC are attached to the tectorial membrane

Inner hair cells

only the inner hair cell stimulation leads to afferent signals

IHC are (probably) displaced by fluid flow

Basilar membrane

• not a membrane in the strict mechanical sense

• still to bending (transversal displacement)

• no axial tension

• acruate zone and pectinate zone: different fiber distribution —> different bending stiffness

• typical displacement on the order of nano to micrometers

• transversal BM displacements as small as 0.1 nm are detectable by humans

Basilar membrane (apex and base)

the width of the basilar membrane increases toward the apex of the cochlea

it is stiffer at the base and softer at the apex

Anatomy of cochlea

spiralled, hollow, conical chamber of bone, structures include:

• scala vestibuli

• scala tympani

• scala media

• helicotrema

• Reissner’s membrane

• basilar membrane

• organ of corti

scala vestibuli

in cochlea- contains perilymph, lies superior to cochlear ducts and abuts the oval window

scala tympani

cochlea- contains perilymph, lies inferior to the scala media and terminates at the round window

scala media

cochlea- contains endolymph, membranous cochlear duct containing the organ of corti

Reissner’s membrane

separates the scala vestibuli from the scala media

basilar membrane

main structural element that determines the mechanical wave propagation properties of the cochlear partition, separates the scala media from the scala tympani

organ of corti

sensory epithelium, a cellular layer on the basilar membrane, powered by the potential difference between the perilymph and endolymph. Lined with hair cells- sensory cells topped with hair-like structures called stereocilia