Measuring strain Measuring strain distributions in tendon - PowerPoint PPT Presentation

Measuring strain Measuring strain distributions in tendon distributions in tendon using confocal microscopy using confocal microscopy and finite elements and finite elements Sam Evans School of Engineering, Cardiff University Hazel Screen Queen Mary University of London

Introduction •Tendon has a complex fibre structure •Highly viscoelastic with sliding of fibres •Tenocytes attached to the fibre bundles are responsible for mechanotransduction •What strains do the tenocytes “see” during loading/relaxation?

Tendon structure Tenocyte Tendon Fascicle Fibril Fibre Tropocollagen Microfibril Crimp Crimping waveform Endotendon 1.5 nm 3.5 nm 50-500 nm 10-50 μ m 50-400 μ m 500-3000 μ m Length scales visualised using confocal microscopy

Methods - experimental •Rat tail tendon samples stained with acridine orange and loaded on the confocal microscope •Held at constant strain (6%) and stress relaxation monitored •Images of cells recorded during relaxation

•Cells and fibres visualised during stress relaxation at constant 6% strain

Methods – image analysis •Cells thresholded out and tracked using IMARIS (Bitplane, Zurich) •Cell coordinates exported to Matlab and incomplete tracks discarded •Tracks smoothed by fitting a second order polynomial through the data points

Cell displacements Frame 0 0 20 40 60 -2 -4 -6 Displacement (pixels)

Strain calculation •We have displacement measurements at discrete points •Strain is the rate of change of displacement with position •Need to interpolate the displacements between the measurement points and find the gradients

Delaunay meshing •If we take three measurement points, we can assume a linear variation in displacement between them •Delaunay meshing always gives the best mesh of triangles joining a set of randomly distributed points •There are still a few very long, thin triangles – these were discarded

Delaunay meshing

Finite elements •The finite element method provides us with the necessary maths in a convenient form •Calculate a B – matrix for each element •Put the displacements in a matrix and multiply by the B – matrix to get the strains

Results Change in strain during relaxation

Number of elements 25 20 15 10 5 0 X: -0.051 ± 0.096 -0.4 -0.32 -0.24 -0.16 -0.08 0 0.08 0.16 0.24 0.32 0.4 Strain in X - direction Number of elements 25 Y: -0.0033 ± 0.114 20 15 XY: -0.0014 ± 0.131 10 5 0 -0.4 -0.32 -0.24 -0.16 -0.08 0 0.08 0.16 0.24 0.32 0.4 Strain in Y- direction Number of elements 25 20 15 10 5 0 -0.4 -0.32 -0.24 -0.16 -0.08 0 0.08 0.16 0.24 0.32 0.4 Shear strain

Discussion •There are very large strains within the tendon during relaxation •These are real movements of the cells, not random errors •The fibres slide, making large strains between adjacent cells •Contraction in x direction due to fluid loss

Conclusions • A good way to find strain distribution from random point displacements • Large strain changes although the overall strain was constant • The cells “see” very different strains from the overall strain • The extracellular matrix is important • Implications for mechanotransduction?