Biomechanics

Question 1

What is the meaning of randomization and replication in study design?

Answer 1

Randomization is using methods to randomly assign study units to control and treatment group. Randomization helps avoid selection bias. Replication is when assigning each treatment to many study units, meaning to perform a variation of a study with the intention to achieve the same result, where some aspects in study has been changed.

Question 2

What is verification and what is validation?

Answer 2

Verification is testing the correctness of mathematical equations implementation, also test for analytical errors. It refers to the process of confirming the accuracy. Validation is testing that the model predict the desired feature, meaning to evaluate and determine if the model or data meets the intended purpose.

Question 3

How is the hydraulic resistance of blood vessels distributed over the cardiovascular system?

Answer 3

The resistance is related to the difference in pressure and the. flow. Since the flow is considered as constant, the resistant will increase when increasing the pressure difference. A severe pressure drop appears when blood flows from arteries into the capillaries. The pressure drops due to the branching into smaller vessels with higher resistance. The pressure is thereafter not changing significantly when flowing from capillaries to the veins, where the resistance is lower.

Question 4

What determines the transport across the wall of micro-vessels?

Answer 4

The osmotic pressure: is the pressure required to prevent net flow. This pressure determines the movement across the wall. It govern the direction and magnitude of the osmotic flow. In osmosis, molecules spontaneously moves from an area of higher concentration to a lower (diffusion) to equalize the concentration on both sides of the membrane.

Hydrostatic pressure: pressure difference between the lumen and interstitium (in and outside the vessel wall)

diffusion and advection
trancytosis

Question 5

Compute the linear vector transformation Aa. Give the index notation

Answer 5

Aij*ai = Aai

Question 6

How is the second Piola-Kirchhoff stress defined? Explain all parameters.

Answer 6

Piola-Kirchhoss stress is a stress used to describe the response of material under deformation. It is defined in context on finite deformation theory and is represented be the deformed material. It is divided into first and second. First: P=JsigmaF^-T, and Second: S=JF^-1sigmaF^-T. Here, F denoted the deformation gradient, sigma the stress matrix and J is the volume ratio (detF = J).

Question 7

What is the characteristic equation of the eigenvalue problem?

Answer 7

det(λI - A)= 0, where A is the matrix where we are searching for the eigenvalues. The eigenvectors are then found through (λI -A)x=0 where x is the eigenvector.

Question 8

Use Voigt notation and provide Hooke’s law in 3D of an isotropic material

Answer 8

see notes

Question 9

Compute the matrix representation of the right and the left Cauchy-Green strains for
simple tension and equi-biaxial tension of an incompressible material.

Answer 9

see notes

Question 10

Describe the mechanical loading that acts at arteries in the body.

Answer 10

Blood pressure, wall shear stress, strain and stretches

Question 11

What is the hemolysis index?

Answer 11

The hemolysis is a blood-damage mechanism where mechanical shear stress is able to rupture or damage the membrane of erythrocytes (red blood cells). The hemolysis index (HI) is the ratio between the plasma-free hemoglobin and the total hemoglobin in the blood.

Question 12

Describe the basic mechanism that results in the non-linear stress-strain properties of
vascular tissue. Draw a sketch that indicates the role of collagen and elastin.

Answer 12

Due to how collagen is arranged in “loose” fiber clusters, the first stage of the loading will only refer to the stiffness of elastin (linear). When the collagen fibers are “straighten” the vascular tissue becomes stiffer and acts more non-linear due to that the collagen is dominating

Question 13

What is the role of residual strain in the vessel wall?

Answer 13

To obtain the same shape in the vessels when unloaded. Minimize the stress load on the wall when normal conditions.

Question 14

Specify the deformation gradient F and the right Cauchy-Green strain C for simple shear
kinematics.

Answer 14

F = [1 γ 0, 010, 001] and C= F^TF = [1+γ^2 γ 0, γ 1 0, 0 0 1]

Question 15

Explain the basic structure and physiological function of the adventitial layer of conduit
arteries.

Answer 15

Structure:
ECM (extra cellular matrix)
- Dense network of collagen fibers (60-80%).
- Less clearly organized than in the media.
- Other connective tissue (10-25%)

Physiological:
- Anchoring blood vessels to surrounding tissues
- Nervous connection to smooth muscle cells in the media
- Synthesis of collagen by fibroblasts
- Protects the media from overextension

Question 16

How is the rate of deformation tensor defined, and what is its meaning? Explain all
parameters.

Answer 16

d = 1/2(F^-TdF^T+dFF^-1) = 1/2(l^T+l), where l=dFF^-1, gradv

Question 17

What is artherosclerosis? Explain the disease’s progression.

Answer 17

Slowly progressing disease if the intima that leads to formation of intimal plaque. It forms at hemodynamic complex segments (low WWS [lower than 0.2 Pa]). High stresses can rupture the plaque cap anf then trigger a thrombo-embolythic event, which can cause cardiac complications.

Question 18

What determines the viscosity of blood and why? Sketch how the blood viscosity depends
on the shear rate.

Answer 18

Hematocrit level, which is the parentage of erythrocytes (red blood cells) in the blood. Red blood cells are the major cellular component of blood, therefore does the viscosity relates to the amount of red blood cells. At low shear rates, the viscosity is higher (increases with higher hemotocrit level)

Question 19

What are principal stresses?

Answer 19

The principal stresses is the stresses at the stress state where all shear stress components are equal to zero.

Question 20

What are smooth muscle cells?

Answer 20

Smooth muscle cells is muscle cells in the vessel wall. It appears in spindle-shaped configuration. They can switch between contractile and synthetic phenotypes.

Question 21

How is the blood pressure distributed in the cardiovascular system?

Answer 21

The pressure is related to the resistance and the flow. It is higher when leaving the heart in the arteries, decrease when entering the capillaries and then stays at a low pressure in the veins back to the heart.

Question 22

Explain methods to estimate arterial compliance.

Answer 22

Pressure decay method
C = Δt/(Rᐧln(p0/p1)), where Δt is the t1-t0, p0 is the pressure at time t0, p1 is the pressure at time t1, R is the resistance. The pressures p0 and p1 are commonly taken at time t0 right after the dicrotic notch, as well as at the time t1 at the end of the diastolic phase.

Question 23

right and the left
Cauchy-Green, Euler-Almansi, Green-Lagrange

Answer 23

Right: C = F^TF
Left: b = FF^T

Euler-Almansi: e = 1/2 (I-b^-1)
Green-Lagrange: E =1/2 (C-I)

Question 24

Explain the basic structure and physiological function of the medial layer of large arteries.

Answer 24

Structure:
The media consist of 30-60% of the smooth muscle cells (SMC). extracellular matrix (ECM) components such as elastin (5-35%), collagen (15-40%), and other connective tissue (15-25%) like proteoglycan (PG).

Physiological:
- Regulate flow by vasconstriction/vasodilation
- Key for the physiological properties, which influences the cardiovascular system function
- Synthesis of connective tissue (collagen and elastin)
- Regulates wall stress by thickness adaption

Question 25

What are known short comings of the two-element Windkessel model?

Answer 25

Neglectence of inertance (Z), which three-element model does.

Question 26

What is objectivity with application to continuum mechanics?

Answer 26

Principle that ensure invariance of physical laws and equations under change in the choice of reference frame or coordinate system. It remains valid and consistent regardless of the observer’s perspective or coordinates system.

Question 27

What are the key parameters in the mechanical activation of blood platelets?

Answer 27

Shear stress and exposure time. At higher exposure time, the activation exposure time is lower than for lower shear stresses.

Question 28

What is the Péclet number and what does it specify?

Answer 28

The ratio between advective and diffusive transport.
Large: solvent moves together with the fluid flow (advection)
Small: it moves independently from the motion of the fluid (diffusion)

Pe = Vd/D, where V is the flow velocity, d is the diameter of the particle and D is the diffusion constant

Question 29

Provide the continuity equation for an incompressible fluid

Answer 29

divv = trd= 0, where v is velocity and d is the rate of deformation tensor.

Question 30

What forces do act on blood particles

Answer 30

Drag force, gravitational and inertia forces, forces related to fluid pressure, forces related to fluid velocity and shear stress, forces from collisions, chemical and electrical forces, segregation effects (Segré-Silberberg effect, Rouleaux formulation etc.), and mixing

Question 31

Give the governing equations for resistance, capacity and inertance (inductivity) used in
Windkessel models?

Answer 31

R = deltaP/Q
C = deltaV/deltaP
Z = (R^-2 + C^2w^2)^-1/2

Question 32

What is polar decomposition?

Answer 32

The motion of the particle can be decomposed into rigid body motion and deformation according to polar decomposition (right or left). The difference between the left and right is whether they describe the motion by first considering the deformation and then the rigid body motion, or the other way.

Question 33

What are the objectives of blood and how is blood composed?

Answer 33

Objectives:
the blood works as the medium in the circulation that transports oxygen, nutrients, and other substances.

Composed:
- Erythrocytes (red blood cells - 50% (42-52% depending on male or female). These transports oxygen
- Leukocytes (white blood cells - 0.7%). These protects the body against infection and diseases and foreign invaders.
- Thrombocytes (platelets - 0.3%). These are involved in the coagulation process of blood
- Plasma (90% water, 9% proteins and molecules, 1% electrolytes). This component consists of a number of digestion products (LDL, HDL etc. which has been related to atheresclorosis)

Question 34

Explain the basic mechanism of the Windkessel principle.

Answer 34

It explains the mechanism of the circulatory system by lumping the characteristics of the system into different types.

Question 35

Explain the different steps of the cardiac cycle

Answer 35

Systolic phase:
heart muscle contracts leading to ejection of blood from the chambers of the heart (refers to the period of time when ventricles [lower chambers] contract to pump into arteries)

Diastole phase:
the heart relaxes, allowing the chambers to expand and fill with blood

Diacrotic notch:
a small dip observed on a pressure wave during the cardiac cycle. It appears immediately following the closure of the aortic valve and marks the beginning of the diastolic phase.

Question 36

What are the hydrostatic and the deviatoric stresses?

Answer 36

Hydrostatic stress: is the volume changing stress. It is the type of stress that acts on an element submerged in a fluid for example, the same normal stresses on all faces. It is the sum of all normal stresses divided by the amount of dimensions considered.

Deviatoric stress: is the remainder when the hydrostatic stress has been removed. All shear stresses are deviatoric. Deviatoric stress represents the non-uniform or anisotropic stress distribution within a material. It describes the differential stress between different directions and is responsible for shape changes and deformation. Deviatoric stress does not affect the volume of the material.

Question 37

Draw characteristic aortic pressure pulse waves of young and old subjects.

Answer 37

young: less stiffer
old: stiffer

Question 38

Write down the micro-channel transport relation at steady state. Explain all parameters.

Answer 38

The micro-channel flux is described by the solute flux Js. At steady state Js is constant.
Js = -Dᐧgrad(c(x)) + c(x)ᐧv
v is the velocity of solute particles.
D is the diffusion constant for solute particles.
c(x) is the solute gradient as a function of position in the micro-channel.

Question 39

What is osmosis?

Answer 39

spontaneous flow solvent across a semipermeable membrane towards a more concentrated solution. (where molecules/particles moves from higher concentration to lower)

Question 40

provide at least three work-conjugate pair of stress and strains

Answer 40

Cauchy: rate of deformation, first Piola-Kirchhoff stress: dF/dt = second Piola-kirchhoff stress: dE/dt

Question 41

Explain the Sterling´s filtration model

Answer 41

Sterling´s filtration model determines the filtration flux through the vessel wall. It is a function of the transcapillary hydrostatic pressure, and the transcapillary coloid osmotic pressure (COP)

qf = Lp(deltap-sigmadeltaPi), where deltap is the hydrostatic pressure difference, sigma is the reflection coefficient, and deltaPi is the osmotic pressure difference

Question 42

Eulerian and Langragian material time derivative

Answer 42

Langragian: D(__)/Dt = partial(__)partial t. The Langragian is mostly used for solids, the material derivative is Equal to the time derivative.

Eulerian: D___/Dt = partial(___)partial t + ___div v. Eulerial adds a convective term since it often monitor fluids, which has flow going in and out of the domain