COMPUTER ASSISTED MINIMAL INVASIVE SURGERY TOWARDS GUIDED MOTOR CONTROLBy: Vinay B Gavirangaswamy

INTRODUCTION

Minimal invasive surgery is practiced over conventional open surgical methods

Advantageous over traditional techniques as it minimizes post operative complications and leave minimum scars on the body

Restricted visibility and dept perception Difficult to acquire required new motor skills Difficult to gain experience to develop

required motor skills Very few or no alternatives other than

performing actual surgery as teaching method

SOLUTION APPROACH

Increased use of sensors to assist in depth perception

Three-dimensional camera system Computer Tomography as substitute for

improved visibility and depth perception Computer simulation to act a simulation tool

using actual instruments

COMPUTER TOMOGRAPHY

“Any method that reconstructs internal structural information within an object by mathematically reconstructing it from a series of projections”.Construction techniques Set of projection Filtered back projection Algebraic reconstruction methods

KEY TERMINOLOGIES

Constructed using linear attenuation coefficient μ

Depends on element composition and density

Volume element (voxel) a value in three dimensional space, is analogous to pixel in 2D image.

Intensity at voxel is calculated by - incident intensity - detected intensity

Sinogram/Radon – View taken from axis position t and at an angle Φ

d

e

I

Idsyx

0

log),( 0IdI

KEY TERMINOLOGIES (CONTD.)

Phantom- construction of a planar figure from view points

Uses rectangular co-ordinate system

Projections from all the views contribute too much to the center of the image, and causes overlap (blurring)

Uses polar co-ordinate system

Inverse transformation removes blurring

Set of ProjectionsFiltered Back Projections

sincos

,2

yxt

dxdyeyxfwtjS

sin,cos

,)(2

vu

dudySyxf evyuxj

ALGEBRAIC RECONSTRUCTION METHODS

Calculation of linear attenuation coefficient is considered as set of simultaneous equations; written in the form

n – number of voxels m – number of projections A – is the matrix of weights x- voxel values b-projection measurements are the b values

mnnm bxA

ALGEBRAIC RECONSTRUCTION METHOD

No single point that represents stable answer

Convergence may not be very fast

When to stop?

Requires small number of view points compared to FBP

FBP view points need to be equally spaced

Acceptable reconstruction is possible through under sampled projections

Can be parallelized*

Disadvantage (iterative method)

Advantages overfiltered back propagation

* Similar to Parallel Implementations of Gaussian elimination Vasilije’s Project

REFENCES

J.C. Russ, The image processing Handbook CRC Press (1992)

Raman Rao, Ronald D. Kriz et al, “Parallel Implementation of the Filtered Back Projection Algorithm for Tomographic Imaging”, Internet: http://www.sv.vt.edu/xray_ct/parallel/Parallel_CT.html, February 8, 2012