Blood Vessel Properties

7/31/2019 Blood Vessel Properties

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Blood vessel properties


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Blood Vessel Structure


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Composition of each layer of a blood

vessel Intima:

Innermost layerContains endothelial cellsBasal lamina (80 nm thick)Subendothelial layer with collagenous bundles, some elastin

Media:

Middle LayerContains mainly smooth muscle cellsCollagenous fibrils (type III collagen)Divided from adventia by elastin layer (elastin is a protein which is very

elastic, can undergo a stretch ratio of 1.6, about 80% strain)

Adventia:

Outermost layer

Collagen fibers (mainly type III, differ in amino acid sequence from I and II)Ground substanceFibroblasts


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Percentage of all the components


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Blood Vessel Mechanical Characterization and

Structure-Function

Collagen contributedmainly to the linear

region of the nonlinearstress-strain curve

Elastin contributedmainly to the toe partof the stress-straincurve.

stress strain curve from a human vena cava


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Residual stress

Even in the unloaded state, there is still stress in theartery.

This state of residual stress is dependent on thethickness and the composition of the artery.

As arteries are remodeled in response to mechanicalstress, the amount of residual stress changes

A mark of the amount of residual stress is how much

the blood vessel will open when cut. Since the blood vessel is under stress, when we cut the

vessel, the stress holding the vessel together isremoved and the blood vessel springs open.


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Residual stress

Different amounts of residual stress are

present in different arteries


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Residual stress

Change in opening angle of the artery, a measure of the change in residualstress.

Early after exposure to higher pressure, the residual stress in the artery was

greater than that of the controls.

After prolonged exposure, the residual stress, as measured by the opening angle

decreased, indicating that the adaptation changes had reduced the residual

stress


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For a more quantitative description of blood vessel mechanics than toeversus linear region, blood vessel can be modeled as a pseudoelasticmaterial using hyperelastic strain energy functions.

In that case, the blood vessel is often described as a cylinder, with stressand strain represented using cylindrical coordinates.

The 2nd Piola-Kirchoff stress tensor and Green-Lagrange strain tensor areused to represent the stress and strain in the blood vessel, respectively

These are denoted below:


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Test set-up to test blood vessels from

Fung's laboratory

The test set-up allows fortorsional, tensile and

pressure testing.

The blood vessel itself must

be kept in a saline bath

during testing.


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Strain energy function.

For a hyperelastic model, strain energy function are to be used.

For blood vessel mechanics, there are two types of strain energy functions

often used. The first form often used is the polynomial form, given below

in terms of cylindrical Green-Lagrange strain components:

where A1 through A7 are material constants and the strains are the same

as those described above.

The second form uses an exponential function:

The above forms neglect shear stress, assuming a very thin vessel. Stress is

calculated by differentiating the strain energy function with respect to the strain

components


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Nonlinear Stress Strain Curves

As can be expected from differences in tissue structures, there are differences inthe constants for the strain energy functions for different arteries.

To gain some insight into how the coefficients in the strain energy function affectthe shape of the stress strain curve the stress strain curve for the Carotid andAorta arteries modeled using a polynomial strain energy function is plotted.

The strain energy function is shown below:

Artery C (KPa) a1 a2 a4

Carotid 2.9 2.5 .46 .176

Upper

Aorta 3.38 2.8 .52 .58


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Sensitivity of stress

To see the sensitivity of stress derived from the strain energyfunction to the parameters in the strain energy function, constant Cis changed from 2.9 to 3.9.

If a1 is increased from 2.5 to 4.5, we get the

following graph:


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Constants in the strain energy function change significantly.

Material constants in proposed strain energy functions can be used to quantify

changes in blood vessel function due to changes in structure.

Thus, the strain energy function becomes a conduit to quantify structure-function

of soft collagenous tissues just as the anisotropic Hooke's law is a way to

quantify bone structure function relationships


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Elastic properties


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Measuring elastic properties


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Blood Vessel Properties

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