Exam questions Flashcards
(44 cards)
What is the role of residual strain in the vessel wall?
Related to the remodelling of the blood vessel wall. Our blood vessels remodel themselves when stress changes. The stress-growth law provides a biomechanical foundation for tissue engineering.
The zero stress state of a blood vessel consists of open-sector segments whose opening angles vary along the longitudinal axis of the vessel. When the homeostatic state of the blood vessel is changed the opening angle will change. Thus, residual stresses are related to the remodeling of the blood vessel wall. Our blood vessel remodels itself when stress changes.
What are smooth muscle cells?
SMCs are present in most contractile organs. They serve as a contractile cell of arteries, arterioles and veins. They appear as spindle-shaped configurations. In blood vessels they are responsible for maintaining blood pressure. In the vessel wall SMCs are mainly aligned in circumferential vessel direction and they communicate with each other through tightor gap-junctions.
Explain the basic structure and physiological function of the adventitial layer of the large arteries?
Consists of:
Extracellular matrix components(Dense network of collagen fibres, and other connective tissue), fibroblasts(about 10%), vasa vasorum and nerves.
Physiological function:
- anchoring blood vessel to surrounding tissues or binds structures together/holds the vessel in relative position.
- nervous connection to SMCs in the medial layer
- synthesis of collagen by fibroblasts
- protect the media from overextension
Draw the hydraulic and electric representations of a three-element Windkessel model. Denote also the introduced parameters.
(((Flow q(t), pressure p(t) describe the system sate)))
ELECTRIC: impedance Za, capacitance C, resistance R
HYDRAULIC: aortic impedance, arterial capacity and vascular bed resistance
TRUE: veins, heart, elastic arteries(aorta), peripheral resistance
How is the rate of deformation tensor defined?
see fig deformation_tensor
can also be written:
d = 0.5( l + l^T)
(where l is the spatial velocity gradient)
How is the blood pressure distributed in the cardiovasular system?
It is higher in the systolic circuits than in the pulmonary circuits. Blood pressure drops beyond large arteries.
In general: higher in the largest vessels, lowest in capillaries …Highest in the aorta.
See fig P_distrib
Detail a generalised Maxwell model. Draw its mechanical representation as well as creep and relaxation responses.
See fig Maxwell
What determines the viscosity of blood and why?
Hematocrit accounts for about 50% of the difference between normal and high blood viscosity. Basically a higher percentage of RBCs to total blood volume, results in thicker blood
Hematocrit = volume RBCs/Total blood volume
Stationary the red blood cells are clumped together and at low shear they start to drift apart and the viscosity decreases. At high shear they elongate in the flow direction which decreases the viscosity even more. Because of that, blood behaves as a non-Newtonian fluid. As such, the viscosity of blood varies with shear rate. Blood becomes less viscous at high shear rates like those experienced with increased flow such as during exercise or in peak-systole. Therefore, blood is a shear-thinning fluid. Contrarily, blood viscosity increases when shear rate goes down with increased vessel diameters or with low flow, such as downstream from an obstruction or in diastole.
How is the first Piola-Kirchoff stress defined?
see fig PK
Transpose of the nominal stress: P = N^T = JsigF^-T
Where sigma is the Cauchy stress tensor, F^-T the transposed inverse of the deformation gradient and J = det F (volume change).
Sketch and explain the basic structures of a sarcomere.
See fig sarcomere
Contractile units in muscles. Composed of long, fibrous proteins as filaments that slide past each other when a muscle contracts or relaxes. Two of the important proteins are myosin, which forms the thick filament, and actin, which forms the thin filament
Explain methods to estimate arterial compliance.
1) C = ΔV/ΔP
2) During the diastolic phase, the flow is 0. The arterial compliance is then determined using the model’s governing equations and either the decay time method or area method.
IN VIVO:
Arterial compliance is an index of the elasticity of large arteries (such as the thoracic aorta) and is an important cardiovascular risk factor!
1) Ultrasound
2) Magnetic Resonance Imaging (MRI)
IN VITRO:
uniaxial and biaxial tensile testing
Why do the Maxwell and Kelvin-Voigt fail to represent a solid?
Maxwell model does not exhibit strain recovery, even at small strains, so it is usually thought of as a fluid model. Kelvin-Voigt does exhibit strain recovery, so qualitatively, it behaves like a solid. However, neither of these models describes the behavior of fluids or solids quantitatively.
KELVIN VOIGT: The deformation of a dashpot connected in parallel to a spring, as in the Kelvin–Voight model, is restricted by the response of the spring to the applied loads. The dashpot in the Kelvin–Voight model cannot undergo continuous deformations. Therefore, the Kelvin–Voight model represents a viscoelastic solid behavior.
MAXWELL: The Maxwell model does not exhibit strain recovery, not even at small strains. The spring is used to represent the elastic solid behavior and there is a limit to how much a spring can deform. The dashpot represent the fluid behavior and is assumed to deform continuously as long as there is a force there to deform them. A force applied will cause both the spring and the dashpot to deform. The deformation of the spring
will be finite but the dashpot will keep deforming as long as the force is maintained. Therefore, the overall behavior of the Maxwell model is more like a fluid than a solid.
What is model verification and validation?
Model validation: The assurance that the model meets its PURPOSE and represents the real system. (Are the correct equations solved – Does the model reflect the
particular feature of the real object?)
Model verification: The evaluation of whether or not the model matches SPECIFICATIONS and assumptions deemed acceptable for the given purpose of application. (Are the equations solved correctly?)
Compute the matrix representation of the deformation gradient, the right and the left Cauchy-Green strains for simple shear.
See fig GL_simple_shear
Deformation gradient: F(X) = dx/dX =
(1 gamma 0 ;
0 1 0;
0 0 1)
right Green-Lagrange strain: C = F^T F =
(1 gamma 0 ;
gamma 1 + gamma^2 0;
0 0 1)
left Green-Lagrange strain: b = F F^T
(1 + gamma^2 gamma 0 ;
gamma 1 0;
0 0 1)
Describe the basic mechanism that causes the typical non-linear properties of vascular tissue. Draw a sketch that indicates the role of collagen and elastin.
see fig collagen_vs_elastin
Elastin is activated first while collagen provides stiffness att higher stress levels. These two properties combined create the following curve.
Provide the Navier-Stokes equation.
see fig Navier_stokes
div sig + f = rho (Dv/Dt)
Frank Starling effect
The Frank Starling effect stipulates that if blood volume of the heart increases then the heart muscle will contract(at the end of the diastolic phase)
..increased filling pressure of the right heart results in increased cardiac output.
Explain the basic structure and physiological function of the medial layer of large arteries.
The medial layer consists of smooth muscle cells (30 - 60%), an extracellular
matrix which is made of elastin fibrins (from elastin sheets 5 - 25%), collagen fibres/bundles (15 - 40%) and other connective tissue like proteoglycan (15 - 25%).
Physiological functions:
• Regulate flows by vasocontriction/vasodilation (Muscular acitivity regulated by autonomous nervous system. Related to physical activity or thermal regulation.)
• Key for the physiological mechanical properties (Cardiovascular system function)
• Synthesis of connective tissue (Collagen, elastin)
• Regulates wall stress by thickness adaption (Tension of a medial lamellar units (MLU) keeps constant at about 2.0 +-0.4 N/m.)
Provide a matrix representation of the engineering strain tensor and detail the
meaning of the different components.
See picture eng_strain.
u = (u1, u2, u3) is the displacement vector and x1, x2 and x3 are the directions in the coordinate system.
Example: epsilon_11 is the change in length in the x1-direction divided by the original length in the same direction.
Give the elasticity tensor for a linear transversely isotropic material.
See fig Elas_LinTranIso
Compute the matrix representation of the deformation gradient, the right and left
Green-Lagrange strains for simple tension.
see fig GL_simple_tension
F = [lam 0 0
0 1/sqrt(lam) 0
0 0 1/sqrt(lam)]
Detail a Kelvin-Voigt model. Draw its mechanical representation as well as creep and relaxation responses.
See fig Kelvin_Voigt
Sketch the dependence of blood viscosity from the shear rate.
see fig blood_shear
How can the Cauchy stress for a general isotropic fluid be written?
see fig Iso_fluid
