2. Residual stress Force remaining in a body when all external loads are removed Gives rise to a residual strain (movement) which can be measured and used to estimate the degree of residual stress In arteries, residual strain can be quantified by measuring opening angle A O B

3. Helps to balance forces within the arterial wall Controls the remodelling process by altering the local loading on VSMC Required to define the zero stress state A O B Why is residual stress important?

4. 0 40 80 120 11.11.2 Circ. Stress  [kPa] Inner Outer Normalised radius No residual stress:  inner /  mean = 6.5 Residual stress:  inner /  mean = 1.4 Residual stress evens out the stresses in the vessel wall

5. Pressurised tubes Heat Cool

6. Steel rod Wet concrete in a mold Stretch steel while Concrete sets When concrete sets, tension in steel bends beam Beam withstands higher Load without bending 16 tons

7. Cross and cupola 700 tons St. Paul’s Cathedral

8. Residual strain in vegetables

10. With thanks to Stephen Gottlieb

11. 1 2 4 3 7 5 6 1 mm 8 Rat aorta

12. 6050403020100 0 40 80 120 160 Age [weeks] Opening angle [°] Rat aorta No sex differences

14. 100806040200 0 100 200 300 Age [yr] Males Females Opening angle [ ° ] Human aorta

15. Where does residual stress reside? Which part of the wall –Selective removal of layers, by lathing frozen specimens Which components of the wall –Selective digestion/destruction experiments, using enzymes to remove elastin/collagen and freezing to destroy muscle

16. Artery lathe

18. Fraction of vessel remaining Opening Angle [degrees] 1.00.50.0 0 100 200 -100 Material removed from outside Material removed from inside Material removed from both sides Localisation of residual strain Greenwald, S. E., et al. (1997). ASME Journal of Biomechanical Engineering 119: 438-444.

19. Original After elastase treatment

20. Original After collagenase treatment

21. Original Minutes after freezing Months after freezing

23. 100806040200 0 50 100 150 200 FROZEN CONTROL Position (%) Opening Angle (°)

24. 0.00 0.25 0.50 0.75 1.00 1.25 CollagenaseElastaseFreezing Entire aorta Thoracic Abdominal OA ratio [Treatment/Control]

25. Residual stress: conclusions Increases with age Greater in men than women Compressive at inner side of vessel wall Tensile at outer side Resides primarily in the elastic component –and to a lesser extent, in muscular component