DESIGN OF COILS FOR MAGNETIC NEURAL STIMULATION.
EFFICIENCY CRITERIA AND TECHNICAL SOLUTIONS
POLITEHNICA University of Bucharest
email:morega@amotion.pub.ro
OBJECTIVE


MAGNETIC
STIMULATION  medical technique applied for neuromuscular rehabilitation,
therapy and stimulation tests. The efficiency of the medical procedure can be enhanced through an adequate design of the electrical equipment. 



METHOD


The MAGNETIC STIMULATION procedure 

Ø
noninvasive, noncontact and painless
alternative to the ELECTRIC STIMULATION (through implanted electrodes) 

Ø
applied on the TARGET
CELLULAR TISSUE (in this model: the peripheral nervous system and spinal
cord) 

Ø
consists of inducing
electric field in relatively good conducting tissues 

It is considered the equivalence between:
ß




TECHNICAL
PROCEDURE


The electric field is produced through
electromagnetic induction in the area of the TARGET CELLULAR TISSUE. The inductor variable magnetic field is generated at
the skin surface, by a currentcarrying winding, the STIMULATING COIL. 



SCOPE
OF THE STUDY


Different forms of the stimulating coils are
compared with regard to several efficiency criteria in order to analyze the
magnitude and spatial distribution of AF and to find the best geometric
configuration of the coil. 

Efficiency
criteria: q
The AF peak value is
maximized and focused on the target area q
The induced electric
field strength is maximized at a specific target area inside the body and
minimized at the skin level 
MATHEMATICAL
MODEL




DOMAIN 

COORDINATE SYSTEM:
(x,y,z) Cartesian coordinate system


SIMPLIFIED MODEL
OF ANATOMICAL TISSUE:
·
a straight nerve
bundle embedded in a homogeneous conductive material;
·
the characteristic
dimensions of anatomical domains are larger than the dimensions of the coils
currently used.


·
(xOy, z=0) plane is
considered the skin surface, ·
the TARGET CELLULAR
TISUUE is a long fiber, parallel to (Ox) axis, embedded in (xOy z<0)
halfspace. 

STIMULATING
COIL: has no restriction to the shape and is placed above the (xOy,
z=0) plane 

MEDIUM
PROPERTIES: (xOy,
z<0) halfspace is a homogeneous conductive medium (s @ 1 S/m) (xOy,
z>0) halfspace is air 







REGIME


Quasistatic regime – the frequency of the excitation current (f <
1kHz) and the usual tissues conductivity lead to a penetration depth much
larger than the characteristic dimensions of anatomical domains. 

ELECTRIC FIELD SOLUTION 

Analytical solution originally derived by
Esselle and Stuchly [Esselle K., Stuchly Maria, Neural Stimulation with Magnetic Fields: Analysis of Induced Electric
Fields, IEEE Trans. on BME, vol. 39, no. 7, 1992, p. 693700] and cited also in other
works. 

Electric field components produced at a specific location P(x,y,z),
by the current element (idl) of
the winding, which is situated at (x_{0},y_{0},z_{0}):




and the expression of the
elementary AF,
_{} is the distance
between (x_{0},y_{0},z_{0}) and (x,y,z); _{} is its projection
on the (xOy, z = 0) plane; m_{0}
is the magnetic permeability of air; _{} is the time derivative of the stimulating current. 

INTEGRATION TECHNIQUE – CHANGE OF VARIABLES 

The contribution of the total amperturns of a certain winding to the electric field solution results by integrating the equations above. 

Change of variables,
convenient for coils with circular
turns The elementary turn * is circular (of radius r) * can rotate by an angle a (maintaining the fix point A) 
_{} _{} _{} 







APPLICATION
1 FOCALIZATION CRITERIUM 

The basic STIMULATING
COIL: 4 circular
turns, of radius r = 0.02 m, and _{} TARGET CELLULAR TISSUE: the
stimulated fiber is embedded within the tissue, at z =  0.01 m RESULTS: negative
peaks of AF produce stimulation (cellular depolarization), while positive peaks of AF produce inhibition (cellular
hiperpolarization) 

CONCLUSION: The quadruple coil has the best
performances and is the easiest in use because the AF peak corresponds to its
center of symmetry. 



APPLICATION 2 ELECTRIC FIELD
CONTROL IN DEPTH OF TISSUE 

Distribution
of the AF in depth of tissue for three types of the stimulating coils




CONCLUSION:
The inclination and radius of turns could provide a good control for the
localization of the AF values in depth of the tissue. AF
at z = 0 rated by AF at z = 0.01 m (the considered target area) is aprox. 2.5 in case (a) 1.8 in case (b) 1.15 in case (c) 

CONCLUSIONS


q
Several forms of stimulating coils were used in MAGNETIC STIMULATION
of the excitable tissue (nerve and muscle long fibers), in order to improve
the distribution of the ACTIVATING FUNCTION (AF). q
The quadruple coils produce the best concentration of the AF at the
TARGET CELLULAR TISSUE, while minimizing the inhibitory effects on
surrounding regions. q
The combination of quadruple coils with horizontal and inclined turns
may result into the control of the electric field strength magnitude and of
the AF in depth of the stimulated tissue.
It may also concentrate the peak values of the AF at the fiber depth
level, rather than at the skin surface. 



FURTHER
STUDY 

q
The refinement of the coils forms by considering quadruple coils with
eccentric turns. This geometry requires a slight modification in the
geometric description of the circular turns. q The computation of the inductance for each specific coil shape; the spatial distribution of turns influences the inductance and, consequently, the waveform of the stimulating current. 