Transcript Michelle Fritz - Oakland University

Electrostriction Effects
During Defibrillation
by Michelle Fritz
Oakland University SMaRT Program
July 28, 2006
Background
During defibrillation a large electrical shock is applied to the heart to
terminate chaotic mechanical and electrical effects caused by fibrillation.
What are the mechanical effects on the heart from the applied electric
field during defibrillation? This has not yet been investigated.
Are these effects significant?
Approximation of the Heart
•The heart is approximated as a
cylinder with radius a in a
uniform electric field.
•Fibers in the cardiac tissue are
taken into consideration, which
cause it to be anisotropicconductivities differ parallel and
perpendicular to the fibers.
Concepts
The electric field causes a
charge distribution inside and
on the outer surfaces of the
heart tissue. This charge
distribution causes mechanical
forces to be exerted on the
tissue in the form of stresses
and strains
As a result of the stresses and
strains, there is a displacement of
tissue. The goal of the following
calculations is to determine how
large this displacement is.
Calculations
Electrical Model
Solve for the potentials Vin r ,   and Vout r ,  
1   V 
1  2V
0
r
   e 2
using  er
2
r r  r 
r 
along with the boundary conditions at r = a,
J or  J er
  o
 e   o 
Vo
V
   er e
r
r
Ve Vo



Mechanical Model
In anisotropic tissue, Gauss’s law relates the charge density to the electric field.
The body forces can be found this way.
     E


F  E
Equations for mechanical equilibrium (Navier’s equations) are used.
 1  3 1  3
p
1  2 
  Fr  0
  2   3

 2
3
2
r
 2r  2r r  2r r 
 1  3 1  2
1 p
1  1  2
1  3 
  F  0

 2 

 2
 3
 2
3
2
2
2 
r 
2r r
2r r r 
2r r 
 2 r
Results
Pressure p and a stream function Ψ are found that satisfy Navier’s
equations and boundary conditions. Once these are found, the components
of the displacement are determined using
1 
Ur  
r r
and
U 

r
By using realistic values for the conductivities and Electric field, numerical
values for the displacement at the surface of the tissue are obtained.
U r  2.2 10 10 m
U  2.4 1010 m